Expected Value Question

Question

In a fast food store’s lucky number contest, 25% of the customers win $1, 10% win $10, 4% win $20 and 1% win $50. Find the expected winnings of a customer.

Answer 1

How much does it cost to enter the contest and play the game?

Is there a "blind bet" where the customer must put some money down?

Let N be the price to play....

0.25 (1-N) + 0.1*(10-N) + 0.04(20-N) + 0.01(50-N) + 0.6(0-N) =

0.25 - 0.25N + 1 - 0.1N + 0.8 - 0.04N + 0.5 - 0.01N - 0.6N =

2.25 - N

So the expected value is Exp(n) = 2.25-n where n is the price to play

Answer 2