# Probability

## Exercise 15.1 Part 2

Question 6: Refer to Table 14.7, Chapter 14 (NCERT Book).

(i) Find the probability that a student obtained less than 20% in the mathematics test.

Answer: Total number of students = 90
Full marks = 100
Number of students with less than 20% marks = 27
Hence, P(E) = 27/90 = 3/10

(ii) Find the probability that a student obtained marks 60 or above.

Answer: Number of students with 60 or more marks = 23
Hence, P(E) = 23/90

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.

OpinionNumber of students
Like135
Dislike65

Find the probability that a student chosen at random

(i) likes statistics,

Answer: Total number of students = 200
Number of students who like statistics = 135
Hence, P(E) = 135/200 = 27/40

(ii) does not like it.

Answer: Number of students who dislike statistics = 65
Hence, P(E) = 65/200 = 13/40

Question 8. Refer to Q.2, Exercise 14.2 (NCERT Book). What is the empirical probability that an engineer lives:

(i) less than 7 km from her place of work?

Answer: Total number of engineers = 40
Number of engineers living at less than 7 km from workplace = 9
Hence, P(E) = 9/40

(ii) more than or equal to 7 km from her place of work?

Answer: Number of engineers living at more than or equal to 7 km from workplace = 31
Hence, P(E) = 31/40

(iii) within ½ km from her place of work?

Answer: Number of engineers living within ½ km = 0
Hence, P(E) = 0

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.

Question 10: Activity: 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.

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: Total number of bags = 11
Less than 5 kg = 2
More than 5 kg = 7
Hence, P(E) = 7/11

Question 12: In Q.5, Exercise 14.2(NCERT Book), 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 = 30
Number of days with sulphur dioxide (ppm) 0.12 – 0.16 = 2
Hence, P(E) = 2/30 = 1/15

Question 13: In Q.1, Exercise 14.2(NCERT Book), 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 with blood group AB = 3
Hence, P(E) = 3/30 = 1/10