Final answer:
The probability of winning the Illinois Pick 4 lottery is 1 in 10,000. If you win, your profit would be $4999. The expected value of your profit per ticket is -$0.50, indicating an average loss of 50 cents per ticket purchased.
Step-by-step explanation:
To find your probability of winning the Illinois Pick 4 lottery game, we consider that there are 10,000 possible number combinations since the game involves picking a sequence of 4 digits. The probability of selecting the correct sequence is 1 in 10,000 since only one of these combinations will be the winning sequence.
For part (b), if you win, your profit would be the amount you collect minus the amount you paid for the ticket. Therefore, your profit would be $5000 (prize) - $1 (cost of the ticket) = $4999.
To find the expected value of your profit for part (c), you use the probability of winning and the profit for winning. The expected value (EV) of the game is calculated by multiplying each outcome by its corresponding probability and summing these products. To calculate the EV in this case:
- You have a 1/10,000 chance of winning $4999.
- You have a 9,999/10,000 chance of losing $1 (since you don't get anything if you don't win).
Therefore, the EV is (1/10,000 * $4999) + (9,999/10,000 * -$1) = $0.4999 - $0.9999 = -$0.50. This means, on average, you would expect to lose 50 cents per ticket purchased.