Important Questions for Chapter 15 - Probability

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Important questions based on NCERT syllabus for Chapter 15 - Probability:

Question 1: A factory manufacturing car batteries made a survey in the field on the life of these batteries. The data obtained was as follows:
Prob
What is the probability that a battery chosen at random

(i) will not last more than 36 months?
(ii) will last for four years?
Solution:
Number of batteries that didn’t las for more than 36 months = 50 + 240 = 290
Probability that the battery will not last more than 36 months = 290/1000 = 0.29

Number of batteries that lasted 4 years = 160
Probability that a battery will last 4 years = 160/1000 = 0.16

Question 2: A survey was conducted to see what people like to do in their free time. 100 people were interviewed. 20 people said they watch TV, 32 said that they read, 27 said they surf the internet and the rest said they do other stuff. Based on the data, what is the probability that a person chose at random
I. likes watching TV
II. likes reading
III. likes surfing the nws
IV. prefers to do something other than these activities.
Solution:
Probability that a person likes watching TV = 20/100 = 0.2
Probability that a person likes reading = 32/100 = 0.32
Probability that a person likes surfing the internet = 27/100 = 0.27
Number of people who like to do something else = 100 – (20 + 32 +0 27) = 21
Probability that a person likes something else = 21/100 = 0.21

Question 3: A group consists of 12 persons, of which 3 are extremely patient, other 6 are extremely honest and rest are extremely kind. A person from the group is selected at random. Assuming that each person is equally likely to be selected, find the probability of selecting a person who is
(i) extremely patient
(ii) extremely kind or honest.
Which of the above values you prefer more?
Solution:
Total number of persons in the group = 12
(i) Number of persons who are extremely patient = 3
P(selecting a person who is extremely patient) = 3/12 = 1/4
(ii) Number of persons who are extremely honest = 6
Number of persons who are extremely kind = 12 - (3 + 6) = 3
∴ P(selecting a person who is extremely kind or extremely honest) = 3+6/12=9/12 = 3/4
From the given three values, we prefer honesty. Honesty can get rid of rampant corruption which is a burning issue of the present society.