Probability
Class 9th Mathematics CBSE Solution
- In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she…
- 1500 families with 2 children were selected randomly, and the following data…
- Refer to Example 5, Section 14.4, Chapter 14 Find the probability that a…
- Three coins are tossed simultaneously 200 times with the following frequencies…
- An organisation selected 2400 families at random and surveyed them to determine…
- Refer to Table 14.7, Chapter 14. (i) Find the probability that a student…
- To know the opinion of the students about the subject statistics, a survey of…
- Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer…
- Activity: Note the frequency of two-wheelers, three-wheelers and four-wheelers…
- Eleven bags of wheat flour, each marked 5 kg, actually contained the following…
- In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution…
- In Q.1, Exercise 14.2, you were asked to prepare a frequency distribution…
Exercise 15.1
Question 1.In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.
Answer:
Total number of balls played = 30
Numbers of boundary hit = 6
Number of times she missed the boundary = 30 – 6
= 24
Hence,
The probability of she didn’t hit a boundary
= 24/30
Divide numerator and denominator by 6 to get,
= 4/5
Question 2.
1500 families with 2 children were selected randomly, and the following data were recorded:
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 = 1500
(i) Numbers of families having two girls = 475
The probability of families having two girls will be,
(ii) Number of families having one girl = 814
The probability of families having one girl will be,
(iii) Number of families having zero girls = 211
The probability of families having zero girls will be,
Sum of probabilities
Hence,
Yes, the sum of these probabilities is 1.
Question 3.
Refer to Example 5, Section 14.4, Chapter 14 Find the probability that a student of the class was born in August.
Answer:
Total numbers of students = 40
Number of students in august = 6
Hence,
The required probability
= 0.15
Hence, Probability of students that are born in the month of August is 0.15
Question 4.
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up
Answer:
Number of times two heads come up = 72
Total number of times the coins were tossed = 200
The probability of the number of times two head come up
Question 5.
An organisation 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:
Total number of families = 2400
(i) Number of families earning Rs. 10,000 – 13,000 per month and owning exactly two vehicles = 29
Hence,
Probability of families earning Rs. 10,000 – 13,000 per month and owning exactly two vehicles will be,
(ii) Number of families earning Rs. 16000 or more per month and owning exactly one vehicle = 579
Hence,
Probability of families earning Rs. 16000 or more per month and owning exactly one vehicle will be,
(iii) Number of families earning less than Rs. 7000 per month and does not own any vehicle = 10
Hence,
Probability of families earning less than Rs. 7,000 per month and doesn’t own any vehicles will be,
(iv) Number of families earning Rs. 13,000-16000 per month and owning more than two vehicles = 25
Hence,
Probability of families earning Rs. 13,000-16000 per month and owning more than two vehicles will be,
(v) Number of families owning not more than 1 vehicle are
= 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1 + 579
= 2062
Hence,
Probability of families owning not more than one vehicle will be
Question 6.
Refer to Table 14.7, Chapter 14.
(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:
Total number of students = 90
(i) Number of students obtained less than 20% in the mathematics test = 7
Hence,
Probability of students obtained less than 20% in mathematics test will be,
(ii) Number of students obtained marks 60 or above = 15 + 8
= 23
Hence,
Probability of students obtained marks 60 or above will be
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.
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 who like statistics = 135
Hence,
Probability of students liking statistics will be
(ii) Number of students who dislike statistics = 65
Hence,
Question 8.
Refer to Q.2, Exercise 14.2. 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 1/2 km from her place of work?
Answer:
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 3 2 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12
Total number of engineers = 40
(i) Number of engineers living less than 7 km from their place of work = 9
Hence,
Probability of engineers living less than 7 km from their place of work will be,
(ii) Number of engineers living more than 7 km from their place of work = 40 – 9
= 31
Hence,
Probability of engineers living more than 7 km from their place of work will be,
(iii) Number of engineers living within � km from her place of work = 0
Hence,
Probability of engineers living within � km from her place of work would be,
Question 9.
Activity: 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:
Activity:
The following data collected is collected in a duration of 1 hour.
Data Collected:
Number of two-wheeler passing = 127
Number of four wheeler passing = 21
Probability that the vehicle is two wheeler is given by,
Question 10.
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:
Total number of bags = 11
Number of bags containing more than 5 kg of flour = 7
Hence,
Probability of bags containing more than 5 kg of flour will be
Question 11.
In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding 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:
Total number of days recorded = 30 days
Number of days in which sulphur dioxide is in the interval 0.12 - 0.16 = 2
Hence,
Probability of days in which SO2 is in the interval 0.12 – 0.16 will be
Question 12.
In Q.1, Exercise 14.2, you were asked to prepare a frequency distribution table regarding 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:
Total number of students = 30
Number of students having blood group AB = 3
Hence,
Probability of students having blood group AB will be,
