40 balls#1-40 are placed in a machine & 8 of them are drawn.If the 8numbers drawn = the numbers that a player chose, the player wins $1,000,000. the order in which the numbers are drawn doesn't matter

Question

Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.

P(win) =

A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.

A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar.

Answer 1

The total number of 8 ball combinations possible - 40 C 8 ( 40 choose 8 ).

Out of these there's one winning combination, so the probability of winning by purchasing 1 lottery ticket - 1/(40C8) (Pretty damn low!)

Single lottery ticket costs - $2

Cost of 10,000 tickets - $20,000

Expected Value to state - return from sale of tickets + loss from win

1. > $20,000 - probability of win * payout - probability of loss * 0
2. $20,000 - (1/40C8)*1000,000 - (1-1/40C8)*0

Expected Value to you ->

-> -cost of purchase + proceeds from payout

-> -$20,000 + probability of payout * payout

-> -$20,000 + (1/40C8)*$1000,000

Note that the expected values net to zero (state vs you) as it's a zero sum game.