There is a group of 10 families each having 5 children of which 2 are boys and 3 are girls. One child is selected from each family, each child of the family being equally likely to be selected. Find the probability that among the 10 children so selected, there are exactly 5 girls.

Solution

Here n = 10
Let p be the probability of success
$therefore space space straight p space equals space straight P left parenthesis selecting space one space girl space out space of space 2 space boys space and space 3 space girls right parenthesis space equals 3 over 5 space space space space space straight q space equals space 1 space minus space straight p space equals space 1 space minus space 3 over 5 space equals space 2 over 5 straight P left parenthesis getting space exactly space 5 space girls right parenthesis space equals space straight P left parenthesis 5 right parenthesis space equals space straight C presuperscript 10 subscript 5 space open parentheses 2 over 5 close parentheses to the power of 5 space open parentheses 3 over 5 close parentheses to the power of 5 space space space space space space space space space space space space space space space space space space equals space fraction numerator 10 cross times 9 cross times 8 cross times 7 cross times 6 space over denominator 1 cross times 2 cross times 3 cross times 4 cross times 5 end fraction cross times 32 over 3125 cross times 243 over 3125 space equals 0.2$

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Probability

There is a group of 10 families each having 5 children of which 2 are boys and 3 are girls. One child is selected from each family, each child of the family being equally likely to be selected. Find the probability that among the 10 children so selected, there are exactly 5 girls.

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