five hundred raffle tickets are sold for $2 each. one prize of $400 is to be awarded. raul purchases one ticket. what is his expected value and fair price of the ticket.

$1000 in and $400 out :)

chance of winning = 1/500
value = 400/500 = 80 cents

To calculate the expected value and fair price of the raffle ticket, we need to understand a few key concepts.

1. Expected Value: The expected value represents the average amount one can expect to win (or lose) per raffle ticket. It is calculated by multiplying the probability of winning by the corresponding prize value and subtracting the cost of the ticket.

2. Fair Price: The fair price of a raffle ticket is the maximum amount a person should be willing to pay for a ticket to make it a fair game. It is calculated by dividing the expected value by the probability of winning.

Let's calculate the expected value and fair price of Raul's ticket step by step:

1. Total amount collected from selling 500 tickets: $2 × 500 = $1000.

2. Probability of winning: Since there is only one prize and 500 tickets sold, the probability of winning is 1 out of 500, or 1/500.

3. Subtract the cost of the ticket ($2) from the prize value ($400): $400 - $2 = $398.

4. Calculate the expected value:
Expected value = (probability of winning) × (prize value - ticket cost)
= (1/500) × ($398)
= $0.796

So, the expected value of Raul's ticket is $0.796.

5. Calculate the fair price:
Fair price = (expected value) / (probability of winning)
= $0.796 / (1/500)
= $398

Therefore, the fair price for the raffle ticket is $398, which means Raul should not pay more than that amount for the ticket if he wants it to be a fair game.

Overall, Raul's expected value is $0.796, indicating that on average, he can expect to win about $0.796 per ticket purchased. However, the fair price for the ticket is $398, which suggests that Raul should only pay up to $398 to ensure the game is fair.