A chain of fast-food restaurants offers an instant-winner promotion. Drink cups and packages of French fries come with peel-off coupons. According to the promotion, 1 in 20 packages is a winner.
(a) A group of friends buys four drinks and three orders of fries. What’s the probability that they win, assuming the prizes are attached to the cups and fry containers independently?
(b) Assuming independence, how many drinks and fries would the group have to order to have a 50% chance of finding a winner?
(c) Use Boole’s inequality to estimate the probability in part (a). Do you expect this approach to work well in this application?