# Assume that the probability that a child is a boy is 0.5. A couple has 3 children. What is the probability that all 3 children are boys? Given that the oldest and the youngest are boys, compute the...

Assume that the probability that a child is a boy is 0.5. A couple has 3 children. What is the probability that all 3 children are boys? Given that the oldest and the youngest are boys, compute the probability that all children are boys. Compute the probability that at least one child is a boy.

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### 1 Answer

Let X , Y , and Z represents respctively oldest , middle and youngest children.

X is boy probabilty = .5

Y is boy probabilty = .5

Z is boy probabilty = .5

P(all boys)= .5 x .5 x .5

=1/8

(ii) when X and Z are boys

P( all boys )= 1/2

because only concern probability is Y ,being boy its probabilty will be .5

(iii) At least one boys

P(at least one boy)=1-P(all girls)

=1- .5 x .5 x.5

=1-1/8

=7/8