Question

A charity raffle sells 2000 tickets for $1 each. Prizes are awarded of one $100, four $50, and eight $25. Find the expected value if you purchase 1 ticket. Your expected value should end up negative since there are way more chances to not win than to win one of the prizes. Expected value is calculated by multiplying every possible outcome by its probability and then adding those products. Let's break this down. a) In this case there are 2000 outcomes. How many expect to be out their dollar and not win anything?

Answer 1

Of the 2000 tickets

1 ticket has a chance to win 100 probability of getting this ticket = 1/2000

similarly

probability of winning 50 = 4/2000

probability of winning 25 = 8/2000

probability of winning nothing = (2000 - (1+8+4))/2000 = 1987/2000

Expected value =

i.e. you spend 1 dollar for every ticket hence if you win 50, your net profit is 49

Hence,

Expected value = (1/2000)*99 + (4/2000)*49 + (8/2000)*24 + (1987/2000)*(-1) = -0.75

On an average you lose 75 cents for every game you play over the long run