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9 September, 00:44

In a class 19 of students, 7 play an instrument and 13 play a sport. There are 4 students who do not play an instrument or a sport. What is the probability that a student who plays an instrument also plays a sport?

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Answers (2)
  1. 9 September, 00:55
    0
    5/7 ≈ 71.4%

    Step-by-step explanation:

    There are 19 students total. 4 of them do not play an instrument or a sport. Which means there are 15 students who play either an instrument and/or a sport.

    Let's say:

    x is the number of students who only play instruments

    y is the number of students who play both instruments and sports

    z is the number of students who only play sports.

    We can use the information to write three equations:

    x + y = 7

    y + z = 13

    x + y + z = 15

    Solve the system of equations with either substitution or elimination. Using elimination, add the first two equations:

    x + 2y + z = 20

    Subtract the third equation:

    y = 5

    Therefore, x = 2 and z = 8.

    So the percent of students who play an instrument who also play a sport is:

    y / (x + y)

    5 / (2 + 5)

    5/7

    ≈ 71.4%
  2. 9 September, 01:07
    0
    Step-by-step explanation:

    7+13=20total

    4/20=1/5 not sure though
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