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

Answer:

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

Step-by-step 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.

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