In a class of 29 students, 20 have a brother and 8 have a sister. There are 3 students who do not have any siblings. What is the probability

Question

In a class of 29 students, 20 have a brother and 8 have a sister. There are 3 students who do not have any siblings. What is the probability that a student chosen randomly from the class is an only child?

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Adela 5 months 2021-08-31T04:54:09+00:00 1 Answers 1 views 0

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    2021-08-31T04:55:57+00:00

    Answer: 1/4 = 0.25 = 25%

    Step-by-step explanation:

    Let x be the number of students having both brother and sister.

    Brother only is 9-x

    Sister only is 16-x

    Brother only + sister only + both + neither = 28

    (9-x) + (16-x) + x + 7 = 28

    32 – x = 28

    x = 4

    The probability per the diagram is 4/16 = 1/4

    Per definition of conditional probability:

    prob( brother | sister) = prob ( brother AND sister) / prob ( sister)

                = 4/16 = 1/4

    1/4 = 0.25 = 25%

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