Question

one thousand raffle tickets are sold for $1.00 each. One prize of $800 is to be awarded.
1. Rena Condos purchases one ticket. Determine her expected value.
2. Determine the fair price of a ticket.

Answer 1

These problems are all basically the same; what's the probability for outcome i (e.g., failure)? What's the reward (negative if cost) for outcome i? Do this for each outcome.

To determine fair price, sum of (probability of outcome i) * (reward for outcome i) = 0... do this for each i, and their total should sum to 0 for a fair game. In this case, we only have two outcomes, for which we can derive their respective probabilities, and they want to know what the price of the ticket should be (so, 800 reward stays the same).

(probability of success) * (reward for success) - (probability of failure) * x = 0, solve for x.