81. In a lottery, there are 250 prizes of $5, 50 prizes of $25, and ten prizes of $100. Assuming that 10,000 tickets are to be issued and sold, what is a fair price to charge to break even

the price of the ticket should be $0.35/ticket

Explanation:

since each ticket in a lottery are equally likely to be chosen, we define the random variable P = gains from the lottery. Then the expected gain is:

E (P) = probability of getting the $5 prize * $5/ticket + probability of getting the $25 prize * $25/ticket + probability of getting the $100 prize * $100/ticket = 250/10000 * $5/ticket + 50/10000 * $25/ticket + 10/10000 * $100/ticket = $0.35/ticket

then if all lottery tickets have the same prize (the lottery tickets are not segmented according to the prizes, where more expensive ticket is associated with the highest prize), then in order to break even the cost of the ticket should be the same that the revenue we get from it, thus

Cost of the ticket = revenue of the ticket = $0.35/ticket