There are 800 families with four children in | vedclass

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Question

(A) Let $n = 4$ be the number of children in each family. The probability of a child being a boy $(B)$ or a girl $(G)$ is $P(B) = P(G) = \frac{1}{2}$.

Vedclass · Accepted Answer

$700$

Vedclass · Answer

(A) Let $n = 4$ be the number of children in each family. The probability of a child being a boy $(B)$ or a girl $(G)$ is $P(B) = P(G) = \frac{1}{2}$.For a family with $4$ children,the total number of possible outcomes is $2^4 = 16$.The event of having children of both sexes is the complement of the event where all children are of the same sex (all boys or all girls).$P(	ext{all boys}) = (\frac{1}{2})^4 = \frac{1}{16}$.$P(	ext{all girls}) = (\frac{1}{2})^4 = \frac{1}{16}$.$P(	ext{both sexes}) = 1 - [P(	ext{all boys}) + P(	ext{all girls})] = 1 - [\frac{1}{16} + \frac{1}{16}] = 1 - \frac{2}{16} = 1 - \frac{1}{8} = \frac{7}{8}$.For $800$ families,the expected number of families with children of both sexes is $800 	imes \frac{7}{8} = 700$.

There are $800$ families with four children in each family. Assuming an equal chance for every child to be a boy or a girl,the number of families expected to have children of both sexes is:

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