Could you hep me solve that problem

Question

a local town decides to hold a charity lottery to raise money for the animal shelter. there will be one grand prize of $20000 and 20 second place prizes of $500. tickets cost $10 each, and 10000 tickets will be sold. calculate the expected value of a single ticket?

Answer 1

You need to calculate the probability of winning each potential prize amount, multiply that probability by the prize value and then add them together.

Grand prize probability = 1/10,000 = .0001 Expected value = .0001 * 20,000 = 2.00

2nd prize probability = 20/10000 = .002 Expected value = .002 * 500 = 1.00

Expected value of one ticket = 2.00 + 1.00 = $3.00

Above is the proper methodology but another way to understand the logic is this:

Total prize money is (20,000 *1) + (500 *20) = 20,000 + 10,000 = 30,000

If there is 30,000 in prize money and 10,000 tickets then each ticket is worth 30,000/10,000 = $3