 # Probability

## There is no content available!

To Access the full content, Please Purchase

• Q1

To know the opinion of the students about the subject Maths, 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 Maths, (ii) does not like it.

Marks:3

Total number of students = 135 + 65 = 200
(i) Number of students liking statistics = 135
P(Students liking Mathematics) = 135/200 = 27/40

(ii) Number of students who do not like statistics = 65
P(students not liking Mathematics) = 65/200 = 13/40.

• Q2

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.

Marks:5

Totalnumber of students = 90

(i) Number of students getting less than 20 % marks in the test = 7

Hence, required probability=7/90.

(ii) Number of students obtaining marks 60 or above

=15 + 8
= 23

Hence, required probability=23/90.

• Q3

100 plants each, were planted in 100 schools during Van Mahotsava. After one month, the no. of plants that survived were recorded as in data below:

 No. of plants survived less than 25 26-50 51-60 61-70 more than 70 total no. of schools No. of schools (frequency) 15 20 30 30 5 100

When a school is selected of random for inspection what is the probability of

(i) more than 25 plants survived in school?

(ii) less than 61 plants survived in the school?

Marks:5

(i)

Total number of school in which plants were planted = 100
No. of schools in which more than 25 plants survived = 20+30+30+5 = 85

P(more than 25 plants survived in the school) = 85/100 = 0.85.
(ii)Total number of schools in which plants were planted = 100
No. of school in which less than 61 plants survived = 15+20+30 = 65
P(less than 61 plants survived) = 65/100 = 0.65.

• Q4

In a cricket match, a batsman hits the ball 24 times out of 72 balls he plays. Find the probability that he did not hit the ball.

Marks:2

Since total number of chances when a batsman can hit a ball = 72

Number of chances when the batsman hit the ball = 24

Number of chances when the batsman did not hit the ball = 72 – 24 = 48

Therefore, Required probability = 48/72 = 2/3.

• Q5

In Cherrapunji, it rains for 200 days in an ordinary year. Find the probability that

(i) there will not be rain in a particular year, (ii) there will be rain in a particular year.

Marks:3