Question

as a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. the first discount choice was 20% off all purchases made that day. the second discount choice was 10% off all purchases for the week. of those who received the discounts, 28 chose the first discount and 22 chose the second discount. one customer will be selected at random from those who received a discount. let ( f ) represent the event that the selected person chose the first discount, and let ( s ) represent the event that the selected person chose the second discount. are ( f ) and ( s ) mutually exclusive events? a yes, because ( p(fcap s)=0 ). b yes, because ( p(fcap s)=0.12 ). c yes, because ( p(fcap s)=1 ). d no, because ( p(fcap s)=0 ). e no, because ( p(fcap s)=1 ).

Explanation:

Mutually exclusive events cannot occur at the same time. Here, a customer can only choose one discount (either the first or the second). So, there is no customer who chose both discounts simultaneously. In probability terms, \(P(F\cap S)\) (the probability of both \(F\) and \(S\) occurring) is \(0\).

Answer:

A. Yes, because \(P(F\cap S) = 0\)