A charity raffle told people that they should expect to win at least $4 for every ticket they purchase.

Question

A charity raffle told people that they should expect to win at least $4 for every ticket they purchase. There were two $50 gift certificates, seven $20 gift certificates, and eleven $15 gift certificates. If there were 150 tickets sold and each ticket sold for $10, were they honest with their customers? If not, how could you make their claim true? Explain/justify your answer.

Answer 1

150 certificates were sold, 2 for 50, 7 for 20, 11 for 15

Expected win = $ 50 x p (50) + $ 20 x p (20) + $ 15 x p (15) = (50 x 2/150) + (20 x 7/150) + (15 x 11/150) = 2.7

As 2.7 < 4 the claim is false.

4 - 2.7 = 1.3

Suppose you offered x more prizes of 50

Then expected win would increase by x . 50 / 150 = x/3.

x/3 = 1.3

x = 3.9

So if you offered 4 more prizes of $ 50, expected win would be above $ 4.00

The entry cost is irrelevant here (if you were talking about expected profit you would need to factor it in)