Question

A community festival sells 20,000 raffle tickets for $10 each. There are 4 possible prize levels. The grand prize is a golf cart valued at $6,000. There are two winners of $1,000, three winners of $500, and ten winners of $100. What is the expected value of a raffle ticket?Round to the nearest cent. Do not round until the final calculation.

Answer 1

Given

Community festival sells 20,000 raffle tickets for $10 each.

4 possible prize levels:

grand prize -$6,000.

two winners of $1,000

three winners of $500

ten winners of $100

Find

Expected value of a raffle ticket

Step-by-step explanation

x = 6000 , P(x) = 1/20000 , xP(x) = 0.3000

x = 1000 ,P(x) = 2/20000 , xP(x) = 0.1000

x = 500 , P(x) = 3/20000 , xP(x) = 0.07500

x = 100, P(x) = 10/20000 , xP(x) = 0.05000

Total xP(x) = 0.3000 + 0.1000 + 0.0750 + 0.0500 = 0.525

`mean=\sum_^xP(x)=0.525`

expected value of a raffle ticket = 0.525 - 1 = - $ 9.48

Final Answer

Therefore, the expected value of a raffle ticket = -$9.48