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:3
    Answer:

    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.

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  • 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
    Answer:

    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.

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  • 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
    Answer:

    (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.

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  • 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
    Answer:

    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.

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  • 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
    Answer:

    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.

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