91Ó°ÊÓ

Determine the probabilities of having (a) at least one girl and (b) at least one girl and one boy in a family of four children, assuming equal probability of male and female birth.

A machine is producing a large number of bolts automatically. In a box of these bolts, \(95 \%\) are within the allowable tolerance values with respect to diameter, the remainder being outside of the diameter tolerance values. Seven bolts are drawn at random from the box. Determine the probabilities that (a) two and (b) more than two of the seven bolts are outside of the diameter tolerance values.