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.
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
(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