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Chapter 15 – Probability

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Page No 283:

Question 1:

In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

Answer:

Number of times the batswoman hits a boundary = 6
Total number of balls played = 30
∴ Number of times that the batswoman does not hit a boundary = 30 − 6 = 24

Question 2:

1500 families with 2 children were selected randomly, and the following data were recorded:
Number of girls in a family
2
1
0
Number of families
475
814
211
Compute the probability of a family, chosen at random, having
(i) 2 girls (ii) 1 girl (iii) No girl
Also check whether the sum of these probabilities is 1.

Answer:

Total number of families = 475 + 814 + 211
= 1500
(i) Number of families having 2 girls = 475
(ii) Number of families having 1 girl = 814
(iii) Number of families having no girl = 211
Therefore, the sum of all these probabilities is 1.

Question 3:

In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:
Find the probability that a student of the class was born in August.

Answer:

Number of students born in the month of August = 6
Total number of students = 40

Question 4:

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
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

Answer:

Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200

Question 5:

An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:
   Suppose a family is chosen, find the probability that the family chosen is
(i) earning Rs 10000 − 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 vehicles.
(v) owning not more than 1 vehicle.

Answer:

Number of total families surveyed = 10 + 160 + 25 + 0 + 0 + 305 + 27 + 2 + 1 + 535 + 29 + 1 + 2 + 469 + 59 + 25 + 1 + 579 + 82 + 88 = 2400
(i) Number of families earning Rs 10000 ­− 13000 per month and owning exactly 2 vehicles = 29
Hence, required probability, 
(ii) Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle = 579
Hence, required probability, 
(iii) Number of families earning less than Rs 7000 per month and does not own any vehicle = 10
Hence, required probability, 
(iv) Number of families earning Rs 13000 ­− 16000 per month and owning more than 2 vehicles = 25
Hence, required probability, 
(v) Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1 + 579 = 2062
Hence, required probability, 

Page No 284:

Question 6:

A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:

Marks
Number of student
0 − 20
20 − 30
30 − 40
40 − 50
50 − 60
60 − 70
70 − above
7
10
10
20
20
15
8
Total
90

(i) Find the probability that a student obtained less than 20 % in the mathematics test.
(ii) Find the probability that a student obtained marks 60 or above.

Answer:

Totalnumber of students = 90
(i) Number of students getting less than 20 % marks in the test = 7
Hence, required probability, 
(ii) Number of students obtaining marks 60 or above = 15 + 8 = 23
Hence, required probability, 

Question 7:

To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table.
Opinion
Number of students
like
dislike
135
65
Find the probability that a student chosen at random
(i) likes statistics, (ii) does not like it

Answer:

Total number of students = 135 + 65 = 200
(i) Number of students liking statistics = 135
(ii) Number of students who do not like statistics = 65

Question 8:

The distance (in km) of 40 engineers from their residence to their place of work were found as follows.
53102025111371231
1910121718113217162
7978351215183
121429615157612
What is the empirical probability that an engineer lives:
(i) less than 7 km from her place of work?
(ii) more than or equal to 7 km from her place of work?
(iii) within km from her place of work?

Answer:

(i) Total number of engineers = 40
Number of engineers living less than 7 km from their place of work = 9
Hence, required probability that an engineer lives less than 7 km from her place of work,
(ii) Number of engineers living more than or equal to 7 km from their place of work = 40 − 9 = 31
Hence, required probability that an engineer lives more than or equal to 7 km from her place of work, 
(iii) Number of engineers living within km from her place of work = 0
Hence, required probability that an engineer lives within km from her place of work, P = 0

Page No 285:

Question 9:

Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

Answer:

This is an activity based question. Students are advised to perform this activity by yourself.

Question 10:

Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

Answer:

This is an activity based question. Students are advised to perform this activity by yourself.

Question 11:

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:

Number of total bags = 11
Number of bags containing more than 5 kg of flour = 7
Hence, required probability, 

Question 12:


Concentration of SO2 (in ppm)
Number of days (frequency )
0.00 − 0.04
4
0.04 − 0.08
9
0.08 − 0.12
9
0.12 − 0.16
2
0.16 − 0.20
4
0.20 − 0.24
2
Total
30

The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.

Answer:

Number days for which the concentration of sulphur dioxide was in the interval of 0.12 − 0.16 = 2
Total number of days = 30
Hence, required probability, 

Question 13:

Blood group
Number of students
A
9
B
6
AB
3
O
12
Total
30
The above frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.

Answer:

Number of students having blood group AB = 3
Total number of students = 30
Hence, required probability, 

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