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Page No 676:

Question 1:

A coin is tossed 1000 times with the following frequencies:
Head: 455, Tail: 545
Compute the probability for each event.

Answer:

The coin is tossed 1000 times. So, the total number of trials is 1000.

Let A be the event of getting a head and B be the event of getting a tail.

The number of times A happens is 455 and the number of times B happens is 545.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have

Page No 676:

Question 2:

Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:
Two heads: 95 times
One tail: 290 times
No head: 115 times
Find the probability of occurrence of each of these events.

Answer:

The total number of trials is 500.

Let A be the event of getting two heads, B be the event of getting one tail and C be the event of getting no head.

The number of times A happens is 95, the number of times B happens is 290 and the number of times C happens is 115.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have

Page No 676:

Question 3:

Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:

Outcome: No head One head Two heads Three heads
Frequency: 14 38 36 12

If the three coins are simultaneously tossed again, compute the probability of:
(i) 2 heads coming up.
(ii) 3 heads coming up.
(iii) at least one head coming up.
(iv) getting more heads than tails.
(v) getting more tails than heads.

Answer:

The total number of trials is 100.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A be the event of getting two heads.

The number of times A happens is 36.

Therefore, we have

(ii) Let B be the event of getting three heads

The number of times B happens is 12.

Therefore, we have

(iii) Let C be the event of getting at least one head.

The number of times C happens is.

Therefore, we have

(iv) Let D be the event of getting more heads than tails.

The number of times D happens is.

Therefore, we have

(v) Let E be the event of getting more tails than heads.

The number of times E happens is.

Therefore, we have

Page No 676:

Question 4:

1500 families with 2 children were selected randomly and the following data were recorded:
 

Number of girls in a family 0 1 2
Number of families 211 814 475

If a family is chosen at random, compute the probability that it has:
(i) No girl
(ii) 1 girl
(iii) 2 girls
(iv) at most one girl
(v) more girls than boys

Answer:

The total number of trials is 1500.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A be the event of having no girl.

The number of times A happens is 211.

Therefore, we have

(ii) Let B be the event of having one girl.

The number of times B happens is 814.

Therefore, we have

(iii) Let C be the event of having two girls.

The number of times C happens is 475.

Therefore, we have

(iv) Let D be the event of having at most one girl.

The number of times D happens is.

Therefore, we have

(v) Let E be the event of having more girls than boys.

The number of times E happens is 475.

Therefore, we have

Page No 676:

Question 5:

In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays.
(i) he hits boundary
(ii) he does not hit a boundary.

Answer:

The total number of trials is 30.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A be the event of hitting boundary.

The number of times A happens is 6.

Therefore, we have

(ii) Let B be the event of does not hitting boundary.

The number of times B happens is.

Therefore, we have

Page No 676:

Question 6:

The percentage of marks obtained by a student in monthly unit tests are given below:
 

Unit test: I II III IV V
Percentage of marks obtained: 69 71 73 68 76

Find the probability that the student gets:
(i) more than 70% marks
(ii) less than 70% marks
(iii) a distinction

Answer:

The total number of trials is 5.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A be the event of getting more than 70% marks.

The number of times A happens is 3.

Therefore, we have

(ii) Let B be the event of getting less than 70% marks.

The number of times B happens is 2.

Therefore, we have

(iii) Let C be the event of getting a distinction.

The number of times C happens is 1.

Therefore, we have

Page No 676:

Question 7:

To know the opinion of the students about Mathematics, a survey of 200 students was conducted. The data is recorded in the following table:
 

Opinion: Like Dislike
Number of students: 135 65

Find the probability that a student chosen at random (i) likes Mathematics (ii) does not like it.

Answer:

The total number of trials is 200.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A be the event of liking mathematics.

The number of times A happens is 135.

Therefore, we have

(ii) Let B be the event of disliking mathematics.

The number of times B happens is 65.

Therefore, we have

Page No 676:

Question 8:

The blood groups of 30 students of class IX are recorded as follows:

A B O O AB O A O B A O B A O O
A AB O A A O O AB B A O B A B O

A student is selected at random from the class from blood donation, Fin the probability that the blood group of the student chosen is:
(i) A
(ii) B
(iii) AB
(iv) O

Answer:

The total number of trials is 30.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A1 be the event that the blood group of a chosen student is A.

The number of times A1 happens is 9.

Therefore, we have

(iii) Let A2 be the event that the blood group of a chosen student is B.

The number of times A2 happens is 6.

Therefore, we have

(iii) Let A3 be the event that the blood group of a chosen student is AB.

The number of times A3 happens is 3.

Therefore, we have

(iv) Let A4 be the event that the blood group of a chosen student is O.

The number of times A4 happens is 12.

Therefore, we have



Page No 677:

Question 9:

Eleven bags of wheat flour, each marked 5 Kg, actually contained the following weights of flour (in kg):
4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00

Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

Answer:

The total number of trials is 11.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Let A1 be the event that the actual weight of a chosen bag contain more than 5 Kg of flour.

The number of times A1 happens is 7.

Therefore, we have

Page No 677:

Question 10:

Following table shows the birth month of 40 students of class IX.
 

Jan. Feb March April May June July Aug. Sept. Oct. Nov. Dec.
3 4 2 2 5 1 2 5 3 4 4 4

Find the probability that a student was born in August.

Answer:

The total number of trials is 40.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Let A1 be the event that the birth month of a chosen student is august.

The number of times A1 happens is 5.

Therefore, we have

Page No 677:

Question 11:

Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.
 

Conc. of SO2 0.00-0.04 0.04-0.08 0.08-0.12 0.12-0.16 0.16-0.20 0.20-0.24
No. days: 4 8 9 2 4 3

Find the probability of concentration of sulphur dioxide in the interval
0.12-0.16 on any of these days.

Answer:

The total number of trials is 30.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Let A1 be the event that the concentration of sulphur dioxide in a day is 0.12-0.16 parts per million.

The number of times A1 happens is 2.

Therefore, we have

Page No 677:

Question 12:

A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below:
 

Monthly income:
(in Rs)
Vehicles per family
0 1 2 Above 2
Less than 7000
7000-10000
10000-13000
13000-16000
16000 or more
10
0
1
2
1
160
305
535
469
579
25
27
29
29
82
0
2
1
25
88

If a family is chosen, find the probability that family is:

(i) earning Rs10000-13000 per month and owning exactly 2 vehicles.
(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than Rs 7000 per month and does not own any vehicle.
(iv) earning Rs 13000-16000 per month and owning more than 2 vehicle.
(v) owning not more than 1 vehicle
(vi) owning at least one vehicle.

Answer:

The total number of trials is 2400.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A1 be the event that a chosen family earns Rs 10000-13000 per month and owns exactly 2 vehicles.

The number of times A1 happens is 29.

Therefore, we have

(ii) Let A2 be the event that a chosen family earns Rs 16000 or more per month and owns exactly 1 vehicle.

The number of times A2 happens is 579.

Therefore, we have

(iii) Let A3 be the event that a chosen family earns less than Rs 7000 per month and does not owns any vehicles.

The number of times A3 happens is 10.

Therefore, we have

(iv) Let A4 be the event that a chosen family earns Rs 13000-16000 per month and owns more than 2 vehicles.

The number of times A4 happens is 25.

Therefore, we have

(v) Let A5 be the event that a chosen family owns not more than 1 vehicle (may be 0 or 1). In this case the number of vehicles is independent of the income of the family.

The number of times A5 happens is

.

Therefore, we have

(vi) Let A6 be the event that a chosen family owns atleast 1 vehicle (may be 1 or 2 or above 2). In this case the number of vehicles is independent of the income of the family.

The number of times A6 happens is

.

Therefore, we have

Page No 677:

Question 13:

The following table gives the life time of 400 neon lamps:
 

Life time
(in hours)
300-400 400-500 500-600 600-700 700-800 800-900 900-1000
Number of lamps: 14 56 60 86 74 62 48

A bulb is selected of random, Find the probability that the  the life time of the selected bulb is:
(i) less than 400
(ii) between 300 to 800 hours
(iii) at least 700 hours.

Answer:

The total number of trials is 400.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A1 be the event that the lifetime of a chosen bulb is less than 400 hours.

The number of times A1 happens is 14.

Therefore, we have

(ii) Let A2 be the event that the lifetime of a chosen bulb is in between 300 to 800 hours.

The number of times A2 happens is.

Therefore, we have

.

(iii) Let A3 be the event that the lifetime of a chosen bulb is atleast 700 hours.

The number of times A3 happens is.

Therefore, we have

Page No 677:

Question 14:

Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory:
 

Wages (in Rs) 110-130 130-150 150-170 170-190 190-210 210-230 230-250
No. of workers 3 4 5 6 5 4 3

A worker is selected at random. Find the probability that his wages are:
(i) less than Rs 150
(ii) at least Rs 210
(iii) more than or equal to 150 but less than Rs 210.

Answer:

The total number of trials is 30.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

(i) Let A1 be the event that the wages of a worker is less than Rs 150.

The number of times A1 happens is.

Therefore, we have.

(ii) Let A2 be the event that the wages of a worker is atleast Rs 210.

The number of times A2 happens is.

Therefore, we have.

(iii) Let A3 be the event that the wages of a worker is more than or equal to Rs 150 but less than Rs 210.

The number of times A3 happens is.

Therefore, we have



Page No 678:

Question 15:

A company selected 4000 households at random and surveyed them to find out a relationship between income level and the number of television sets at home. The information so obtained is listed in the following table.
 

Monthly income (in ₹) Number of televisions per household
0 1 2 Above 2
<10,000
10,000 - 14,999
15,000 - 19,999
20,000 - 24,999
25,000 and above
20
10
0
0
0
80
240
380
520
1100
10
60
120
370
760
0
0
30
80
220

Find the probability:
(i) of a household earning ₹ 10,000-14,999 per year and owning one television.
(ii) of a household earning ₹ 25,000 and more per year and owning 2 televisions.
(iii) of a household not having any television.

Answer:

Given: Total events = 4,000
(i) A household earn ₹ 10,000 – ₹ 14,999 per year and have exactly one television.

Favourable Outcome = 240
Required Probability=2404,000=350=0.06

(ii) A household earn ₹ 25,000 and more and owning two televisions.
Favourable Outcome = 760
Required Probability=7604,000=0.19
 
(iii) Household having no television.
Favourable outcome = 20 + 10
= 30
Probability=304,000=3400

Page No 678:

Question 16:

Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the following table:
 

Sum 2 3 4 5 6 7 8 9 10 11 12
Frequency 14 30 42 55 72 75 70 53 46 28 15

If the dice are thrown once more, what is the probability of getting a sum
(i) 3?
(ii) more than 10?
(iii) less than or equal to 5?
(iv) between 8 and 12?

Answer:


(i)
Pgetting a sum 3=30500=350=0.06

 
(ii)
Pgetting a sum more than 10=Pgetting a sum of 11+Pgetting a sum 12=28500+15500=43500=0.086

(iii) 
Pgetting a sum less than or equal to 5=Pgetting a sum of 5+Pgetting a sum of 4+Pgetting a sum of 3+Pgetting a sum of 2=55500+42500+30500+14500=141500=0.282

(iv)
Pgetting sum between 8 and 12=Pgetting sum of 9+Pgetting sum of 10+Pgetting a sum of 11=53500+46500+28500=127500=0.254

Page No 678:

Question 17:

A recent survey found that the ages of workers in a factory is distributed as follows:
 

Age (in years) 20-29 30-39 40-49 50-59 60 and above
Number of workers 38 27 86 46 3

If a person is selected at random, find the probability that the person is;
(i) 40 years or more
(ii) under 40 years
(iii) having age from 30 to 39 years
(iv) under 60 but over 39 years

Answer:

(i) P(person is 40 year or more) = P(person having age 40 to 49 years) + P(person having age 50 to 59 years) + P(person having age 60 and above)

 =86200+46200+3200=135200=0.68

(ii) P(person is under 40 years) = P(person having age 20 to 29 years) + P(person having age 30 to 39 years)
=38200+27200=65200=0.33

(iii) P(age form 30 to 39 years) = 27200=0.135

(iv) P(person having age under 60 but over 39 years) = P(person having age 40 to 19 years) + P(person having age 50 to 59 years)
     =86200+46200=132200=0.66

Page No 678:

Question 18:

Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the following table:
 

Number of defective bulbs 0 1 2 3 4 5 6 more than 6
Frequency 400 180 48 41 18 8 3 2

One carton was selected at random. What is the probability that it has
(i) no defective bulb?
(ii) defective bulbs from 2 to 6?
(iii) defective bulbs less than 4?

Answer:


(i) P(no defective bulbs)
=400700=47

(ii) Number of outcomes = 48 + 41 + 18 + 8 + 3 = 118

P(defective bulb from 2 to 6) 
=118700=59350

(iii) Number of outcomes = 400 + 180 + 48 + 41 = 669

P(defective bulb less than 4)=669700

Page No 678:

Question 19:

Over the past 200 working days, the number of defective parts produced by a machine is given in the following table;
 

No. of defective parts 0 1 2 3 4 5 6 7 8 9 10 11 12 13
Days 50 32 22 18 12 12 10 10 10 8 6 6 2 2

Determine the probability that tomorrow's output will have
(i) no defective
(ii) at least one defective part
(iii) not more than 5 defective parts
(iv) more than 13 defective parts

Answer:

Number of possible outcomes = 200

(i)
PNo defect=50200=0.25

(ii) The probability of at-least 1 defect  = 1 – P(no defect)
                                                               = 1 – 0.25
                                                               = 0.75

(iii) Probability that there will be maximum 5 defects = P(0 defect) + P(1 defect) + P(2 defect) + P(3 defect) + P(4 defect) + P(5 defect)

=50200+32200+22200+18200+12200+12200=0.73

(iv) P(more than 13 defective parts) = 0200=0



Page No 679:

Question 1:

Define a trial.

Answer:

What is the meaning of trial?

The word trial means a test of performance, qualities, or suitability.

Definition:

Any particular performance of a random experiment is called a trial. That is, when we perform an experiment it is called a trial of the experiment.

By experiment or trial, we mean a random experiment unless otherwise specified. Where you are required to differentiate between a trial and an experiment, consider the experiment to be a larger entity formed by the combination of a number of trials.

To illustrate the definition, let us take examples:

1. In the experiment of tossing 4 coins, we may consider tossing each coin as a trial and therefore say that there are 4 trials in the experiment.

2. In the experiment of rolling a dice 5 times, we may consider each rolls as a trial and therefore say that there are 5 trials in the experiment.

Note that rolling a dice 5 times is same as rolling 5 dices each one time. Similarly, tossing 4 coins is same as tossing one coin 4 times.

Page No 679:

Question 2:

Define an elementary event.

Answer:

What are the meanings of elementary event?

The word elementary means simple, non decomposable into elements or other primary constituents and the word event means something that result.

Definition:

An elementary event is any single outcome of a trial. Elementary events are also called simple events.

To illustrate the definition, let us take examples:

1. In the experiment of tossing a coin, the possible outcomes H and T. Any one outcome like H is called an elementary event.

2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is called an elementary event.

Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.

Page No 679:

Question 3:

Define an event.

Answer:

What are the meanings of event?

The word event means something that result.

Definition:

An event is a collection of outcomes of a trial of a random experiment.

To illustrate the definition, let us take examples:

1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. Any one outcome like HH is called an event (elementary event). The collections like {HH, HT}, {HH, HT, TT} etc are all events (compound event).

2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Any one outcome like 4 is called an event (elementary event). The collections like {1, 2}, {1, 2, 3}, {2, 5, 6}, {2, 3, 4, 5} etc are all events (compound events).

Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.

Page No 679:

Question 4:

Define probability of an event.

Answer:

The probability of an event denotes the relative frequency of occurrence of an experiment’s outcome, when repeating the experiment.

Definition:

The empirical or experimental definition of probability is that if n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials, then the probability of happening of event A is denoted byand is given by

To illustrate the definition, let us take examples:

1. When two coins are tossed simultaneously, the possible outcomes are HH, HT, TH and TT. The total number of trials is 4. Let A be the event of occurring exactly two heads. The number of times A happens is 1. So, the probability of the event A is

2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Let A be the event of occurring a number greater than 3. The total number of trials is 6. The number of times A happens is 3. So, the probability of the event A is

Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.

Page No 679:

Question 5:

A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is 25, find the number of red balls in the bag.

Answer:

The number of white balls is 4. Let the number of red balls is x. Then the total number of trials is.

Let A be the event of drawing a white ball.

The number of times A happens is 4.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have.

But, it is given that. So, we have

Hence the number of red balls is.

Page No 679:

Question 6:

A die is thrown 100 times. If the probability of getting an even number is 25. How many times an odd number is obtained?

Answer:

The total number of trials is 100. Let the number of times an even number is obtained is x.

Let A be the event of getting an even number.

The number of times A happens is x.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have.

But, it is given that. So, we have

Hence an even number is obtained 40 times. Consequently, an odd number is obtainedtimes.

Page No 679:

Question 7:

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
 

Outcome 3 heads 2 heads 1 head No head
Frequency 23 72 77 28

Find the probability of getting at most two heads.

Answer:

The total number of trials is 200.

Let A be the event of getting at most two heads.

The number of times A happens is.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have.

Page No 679:

Question 8:

In Q.No. 7, what is the probability of getting at least two heads?

Answer:

The total number of trials is 200.

Let A be the event of getting atleast two heads.

The number of times A happens is.

Remember the empirical or experimental or observed frequency approach to probability.

If n be the total number of trials of an experiment and A is an event associated to it such that A happens in m-trials. Then the empirical probability of happening of event A is denoted byand is given by

Therefore, we have

Page No 679:

Question 1:

Fill In The Blanks 

If an experiment does not produce the same outcomes every time but the outcomes in a trial is one of the several possible outcomes, then it is called an ________ experiment. 

Answer:


If an experiment does not produce the same outcomes every time but the outcomes in a trial is one of the several possible outcomes, then it is called an __random__ experiment.

Page No 679:

Question 2:

Fill In The Blanks 

An outcome of a trial of a random experiment is called an _________ event. 

Answer:


An outcome of a trial of a random experiment is called an __elementary__ event. 



Page No 680:

Question 3:

Fill In The Blanks 

A collection of two or more possible outcomes (elementary events) of a trial is called a ________ event. 

Answer:


A collection of two or more possible outcomes (elementary events) of a trial is called a __compound__ event. 

Page No 680:

Question 4:

Fill In The Blanks 

In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability, that the person has a high school certificate is _______.

Answer:


Number of people in the sample study = 642

Number of people having high school certificate = 514

∴ P(Person selected at random has a high school certificate)

= Number of people having high school certificateNumber of people in the sample study

= 514642

= 257321

Thus, the probability that the person selected at random has a high school certificate is 257321.

In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability, that the person has a high school certificate is      257321     .

Page No 680:

Question 5:

80 bulbs are selected at random from a lot and their life time (in hrs) is recorded in the form of following frequency table: 
 

Life time (in hrs): 300 500 700 900 1100
Frequency : 10 12 23 25 10

One bulb is selected at random from the lot. The probability that its life is 1150 hours is __________.

Answer:

Disclaimer: Data given in the question is wrong.

Number of bulbs in the lot = 80

Number of bulbs having life time 1150 hours = 0

∴ P(Bulb selected at random has life time 1150 hours)

= Number of bulbs having life time 1150 hoursNumber of bulbs in the lot

= 080

= 0

Thus, the probability that a bulb selected at random from the lot has life time 1150 hours is 0.

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Question 6:

Fill In The Blanks 

In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat patato chips. If a child is selected at random, the probability that he/she does not like eat patato chips, is _________.

Answer:


Number of children in the survey = 364

Number of children who liked to eat potato chips = 91

∴ Number of children who did not liked to eat potato chips

= Number of children in the survey − Number of children who liked to eat potato chips

= 364 − 91

= 273

Now,

P(A child selected at random does not like to eat potato chips)

= Number of children who did not liked to eat potato chipsNumber of children in the survey

= 273364

= 34

Thus, the probability that a child selected at random does not like to eat potato chips is 34.

In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like eat potato chips, is      34     .

Page No 680:

Question 7:

Fill In The Blanks 

In Q.No. 5, the probability that a bulb selected at random from the the lot has life less than 900 hours is _________.

Answer:


Number of bulbs in the lot = 80

Number of bulbs having life time less than 900 hours

= Number of bulbs having life time 300 hours + Number of bulbs having life time 500 hours + Number of bulbs having life time 700 hours

= 10 + 12 + 23

= 45

∴ P(Bulb selected at random has life time less than 900 hours)

= Number of bulbs having life time less than 900 hoursNumber of bulbs in the lot

= 4580

= 916

Thus, the probability that a bulb selected at random from the lot has life time less than 900 hours is 916.

The probability that a bulb selected at random from the the lot has life less than 900 hours is      916     .

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Question 8:

Fill In The Blanks 

Two coins are tossed 1000 times and outcomes are recorded as below: 

Numbers of heads:      2      1      0
Frequency:                 200  550  250

The probability of getting at most one head is _______.

Answer:


Two coins are tossed 1000 times.

∴ Total number of trials = 1000

Let E be the event of getting at most one head on the two coins.

Number of trials for getting at most one head

= Frequency of getting 0 heads + Frequency of getting 1 head

= 250 + 550

= 800

∴ Probability of getting at most one head = P(E) = Number of trials for getting at most one headTotal number of trials=8001000=45

Thus, the probability of getting at most one head is 45.

The probability of getting at most one head is      45     .

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Question 9:

Fill In The Blanks 

In a medical examination of students of a class, the following blood groups are recorded: 

Blood group:                A      AB      B      O
Number of students:     10      13      12      5

A student is selected at random from the class. The probability that he/she has blood group B, is __________.

Answer:


Total number of students in the class = 10 + 13 + 12 + 5 = 40

Number of students having blood group B = 12

∴ P(A student selected at random has blood group B)

= Number of students having blood group BTotal number of students in the class

= 1240

= 310

Thus, the probability that a student selected at random from the class has blood group B is 310.

A student is selected at random from the class. The probability that he/she has blood group B, is      310     .

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Question 10:

Fill In The Blanks 

A die is thrown 1000 times and the outcomes were recorded as follows: 

Outcomes:      1        2      3      4      5      6
Frequency:     180  150  160  170  150  190

If the die is thown once more, then the probability that its show 5 is _________. 

Answer:


It is given that a die is thrown 1000 times.

∴ Total number of trials = 1000

Let E be the event that the die shows 5.

Number of trials of getting 5 on the die = Frequency of getting 5 on the die = 150

∴ P(Die shows the number 5) = P(E) = Number of trials of getting 5 on the dieTotal number of trials=1501000=320

Thus, the probability that die shows 5 is 320.

If the die is thrown once more, then the probability that its show 5 is      320     



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