probability question (1 Viewer)

poptarts12345 · Apr 10, 2021

There are 4 families and each family has 4 children. Assume the probability of having a boy or girl is 1/2. Determine the probability that exactly 2 of the families will have exactly 2 boys and 2 girls as children.

Answer : 675/2048

Trebla · Apr 10, 2021

Since there is a hierarchy, start with a single family first. The probability that a single family will produce 2 boys and 2 girls is

$\binom{4}{2}\left(\dfrac{1}{2}\right)^2\left(\dfrac{1}{2}\right)^2$

This gives a 3/8 probability that there will be 2 boys and 2 girls. Therefore there is a 5/8 probability that a family will NOT have 2 boys or girls.

Out of the 4 families, the probability that 2 of them will have 2 boys and 2 girls is

$\binom{4}{2}\left(\dfrac{3}{8}\right)^2\left(\dfrac{5}{8}\right)^2$

probability question (1 Viewer)

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