16 4 pts A charity organization is selling 5 raffle tickets

16) (4 pts) A charity organization is selling $5 raffle tickets as part of a fundraiser. The first prize is a trip to Mexico valued at $3250, and the second prize is a weekend spa package valued at $750. The remaining 20 prizes are $25 gas cards. The number of tickets sold is 6000. You bought one ticket. What is your expected net gain?

Solution

Probability of winning first prize = 1/6000

Probability of winning second prize = 1/6000

Probability of winning one of 20 prizes = 20/6000

Probability of winning no prize = (6000-22)/6000 = 5978/6000

Expected price of winning = 3250*1/6000 + 750*1/6000 + 25*20/6000 + 0*5978/6000 = 4500/6000 = 3/4 = 0.75

Expected net gain = 0.75-5 = -4.25 (so loss of 4.25)