Probability
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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:3Answer:
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:5Answer:
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
= 23Hence, 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
2650
5160
6170
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:5Answer:
(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 = 85P(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:2Answer:
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:3Answer:
Since total number of days in an ordinary year = 365
Number of days when it rains in Cherrapunji = 200
Therefore, number of days when there is no rain in Cherrapunji = 365 – 200 = 165
(i) P(there will be rain no in a year) = 165/365 = 33/73
(ii) P(there will be rain in a year)=200/365 = 40/73.