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16 February, 02:51

A couple plans to have two children. Each child is equally likely to be a girl or boy, with gender independent of that of the other child. a. Construct a sample space for the genders of the children, using B for boy and G for girl. b. Find the probability that both of the children are girls. c. Answer part b if, in reality, for a given child, the chance of a girl is 0.48.

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  1. 16 February, 04:44
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    a)

    G - G

    G - B

    B - B

    B - G

    b) 25% probability that both of the children are girls.

    c) 23.04% probability that both of the children are girls.

    Step-by-step explanation:

    a. Construct a sample space for the genders of the children, using B for boy and G for girl.

    B for boy

    G for girl

    Each child can be a boy or a girl

    Two children

    First child - Second child

    G - G

    G - B

    B - B

    B - G

    b. Find the probability that both of the children are girls.

    Two children

    Each has a 50% probability of being a girl

    So

    0.5*0.5 = 0.25

    25% probability that both of the children are girls.

    c. Answer part b if, in reality, for a given child, the chance of a girl is 0.48.

    Two children

    Each has a 48% probability of being a girl

    So

    0.48*0.48 = 0.2304

    23.04% probability that both of the children are girls.
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