Question

A raffle sells 10,000 tickets. Each ticket is sold for $50. Below is a list of prizes and the number of that type of prize. 1 Grand Prize: Toyota Yaris - Value: $17,750 100 Second place prizes: Nintendo Switch with Games: $500 1000 Third Place Prizes: A Box of Frosted Lucky Charms: $4 How much money do the organizers of the event expect to make for every ticket they sell? Note: This question is asking you to find the expected value of a discrete random variable.

Answer 1

here below is pmf of net gain X for each ticket sold:

P(X=-17750+50) =P(X=-17700) =P(grand prize) =1/10000

P(X=-500+50)=P(X=-450) =P(2nd prize )=100/10000

P(X=4+50) =P(X=46)=1000/10000

P(X=50) =P(no prize )=8998/10000

therefore expected value   for every ticket they sell

E(X)= $\sum$ xP(x)=-17700*(1/10000)-450*100/10000+46*1000/10000+50*8899/10000 =42.825