Question

there is a raffle with 500 tickets. one ticket will win a $640 prize, and the remaining tickets will win nothing. if you have a ticket, what is the expected payoff?

Explanation:

Step1: Determine probabilities

The probability of winning the prize ($P(win)$) is the number of winning tickets divided by total tickets. There is 1 winning ticket out of 500, so $P(win) = \frac{1}{500}$. The probability of not winning ($P(lose)$) is $1 - \frac{1}{500} = \frac{499}{500}$.

Step2: Determine payoffs

The payoff for winning ($X_{win}$) is $640$, and the payoff for losing ($X_{lose}$) is $0$.

Step3: Calculate expected value

The formula for expected value ($E(X)$) is $E(X) = P(win) \times X_{win} + P(lose) \times X_{lose}$. Substituting the values: $E(X) = \frac{1}{500} \times 640 + \frac{499}{500} \times 0$. Simplify: $E(X) = \frac{640}{500} = 1.28$.

Answer:

$1.28$