Final answer:
John's expected gain from buying a $1 raffle ticket with a chance to win a $500 prize out of 1,000 tickets sold is negative 50 cents, meaning on average he would lose 50 cents per ticket.
Step-by-step explanation:
John bought one $1 raffle ticket to win a prize worth $500. If 1,000 tickets were sold and each ticket has an equal chance of winning, we need to calculate John's expected gain. To find the expected gain, we multiply the value of the prize by the probability of winning and subtract the cost of the ticket.
The probability of John winning the prize is 1 in 1,000, or 0.001 since there are 1,000 tickets. His expected gain if he does win is $500. Thus, the expected value of winning is:
Expected gain from winning = Prize value × Probability of winning
= $500 × 0.001
= $0.50
Now, we subtract the cost of the ticket to find the net expected gain:
Net expected gain = Expected gain from winning - Cost of ticket
= $0.50 - $1.00
= -$0.50
Therefore, John's expected gain is negative 50 cents. This means, on average, he would lose 50 cents per raffle ticket purchased.