Question

Five thousand tickets are sold at​ $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as​ follows: 1 prize of ​$800​, 3 prizes of ​$200​, 5 prizes of ​$50​, and 20 prizes of​ $5. What is the expected value of this raffle if you buy 1​ ticket?

Answer 1

The expected value of this raffle if you buy 1​ ticket is $0.41.

Explanation:

The expected value of the raffle if we buy one ticket is the sum of the prizes multiplied by each of its probabilities.

This can be written as:

`E(X)=\sum p_iX_i`

For example, the first prize is $800 and we have only 1 prize, that divided by the number of tickets gives us a probability of 1/5000.

If we do this with all the prizes, we can calculate the expected value of a ticket.

`E(X)=\sum p_iX_i\\\\\\E(X)=(1\cdot800+3\cdot200+5\cdot50+20\cdot20)/(5000)\\\\\\E(X)=(800+600+250+400)/(5000)=(2050)/(5000)=0.41`