In a lottery, 3,000,000 tickets are sold each week for 50 cents apiece. Out of those 3,000,000 tickets, 12,006 are drawn at random and without replacement and awarded prizes: twelve thousand $25 prizes, four $10,000 prizes, one $50,000 prize, and one $12,000 prize. If you purchased a single ticket each week, what is the expected value of this game to you?
2007-02-01 13:44:25 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
(12000/3000000)*25+(4/3000000)*10000 + (1/3000000)*50000
=13 cents
But since you spent 50 cents to purchase this ticket, the expected gain from this ticket is actually a los of 37 cents.
2007-02-01 13:51:28 · answer #1 · answered by bruinfan 7 · 0⤊ 0⤋
You find the probability of winning each prize, multiply it by the prize value, add these up, then add -.50 for the 5o cents it costs to buy the ticket.
So (12000/3000000)(25) + (4/3000000)(10000) + (1/3000000)(50000) + (1/3000000)(12000) - .50
2007-02-01 21:49:27 · answer #2 · answered by hayharbr 7 · 0⤊ 0⤋
12,000/3,000,000* $25 + 4/3,000,000 * $10,000 + 1/3 mil *$62k = 0.13
It would seem to cost 37 cents a week to play.
2007-02-01 21:54:33 · answer #3 · answered by LGuard332 2 · 0⤊ 0⤋