Question

A father and his son entered a competition, the probability that the father wins a prize is 1/7, and that his son wins a prize is 2/5. Find the probability that

(1). Either of them (but not both) wins a prize.

(2). At least one of them wins a prize.

Answer 1

(1) $P=\frac{1}{7}*(1-\frac{2}{5})+\frac{2}{5}(1-\frac{1}{7})=\frac{3}{7}.$

(2) $P(F\cup S)=P(F)+P(S)-P(F\cap S)=\frac{1}{7}+\frac{2}{5}-\frac{1}{7}*\frac{2}{5}=\frac{17}{35}.$