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15 October, 02:49

In a class 27 of students, 10 play an instrument and 11 play a sport. There are 13 students who do not play an instrument or a sport. What is the probability that a student does not play an instrument given that they play a sport?

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  1. 15 October, 03:16
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    Step-by-step explanation:

    Total students = 27

    A = students playing instrument

    n (A) = 10

    B = students playing sport

    n (B) = 11

    (A∪B) ' = students who do not play an instrument or a sport

    n (A∪B) ' = 13

    n (A∪B) = 27 - 13 = 14

    n (A∩B) = n (A) + n (B) - n (A∪B)

    = 10 + 11 - 14 = 21 - 14

    = 7

    No. of students playing only instrument = 10 - 7 = 3

    No. of students does not play an instrument given that they play a sport = 11 - 7 = 4

    P (No. of students does not play an instrument given that they play a sport) = 4/27
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