Question

In a raffle where 9000 tickets are sold for $2 each, one prize of $2300 will be awarded. What is the expected value of a single ticket in the raffle?State your answer in terms of dollars rounded to the nearest cent (hundredth).

Answer 1

Answer: -0.74 cents

Using the formula:

$E(x)=\Sigma xP(x)$

Where:

x = value of an outcome

P(x) = probability of that outcome

For the given problem, we have 9000 tickets, out of which one will win a prize of 2300. That means that 8999 people will pay $2, with a probability of 8999/9000 losing, and the winner will get a value of $2300-$2 = $2298 with a probability of 1/9000 winning.

Expressing these into the equation:

$E(x)=(-1)(\frac{8999}{9000})+(2298)(\frac{1}{9000})$$E(x)=-0.7445\approx-0.74$

Therefore, the expected value is -0.74 cents.