Richard is deciding whether to buy a state lottery ticket. Each ticket costs $1, and the probability of winning payoffs is given as follows:
| Probability | Return |
| 0.5 | $0.0 |
| 0.25 | $1.00 |
| 0.2 | $2.00 |
| 0.05 | $7.5 |
- What is the expected value of Richard’s payoff if he buys a lottery ticket? What is the variance?
- Richard’s nickname is “No-Risk Rick” because he is an extremely risk-averse individual. Would he buy the ticket?
- Suppose Richard was offered insurance against losing any money. If he buys 1000 lottery tickets, how much would he be willing to pay to insure his gamble?
- In the long run, given the price of the lottery tickets and the probability/return table, what do you think the state would do about the lottery?
