Probabiity Question

Question

There is one $5050.00 winner in a lottery of 100 tickets. If a ticket costs $50, what is the expected value for the lottery?

x (the amount of money taken home) Probability of the event happening

Win

Lose

What is the expected value?

Is the game fair?

1. No, the mean is zero
2. No, the mean is not zero
3. No, the standard deviation is not 1
4. Yes, the mean is zero
5. Yes, the mean is positive
6. No, the mean is negative

Answer 1

expected winnings is [99(0) + 1(5050)]100 = 5050/100= 50.5. you pay 50 so the expected net winning = 50 cents

It's a more than fair game, but not by much. $5000 in tickets are sold and the payout > the cost of tickets by $50. Whoever runs this lottery will lose $50, not counting the cost of doing the lottery.

but the median outcome is a loss of $50. the mode = $50 loss. Play this lottery, you'll probably lose.

the mean outcome is the average of 99 x -$50 + $5050-$50 all divided by 100

= -4950 + 5000 = $0.50 = 50 cents >0 the mean is positive

while the standard deviation is not = 1, that doesn't make the lottery "unfair"