SOLUTION: How do you solve: In one version of the game keno, the house has a pot containing 80 balls, numbered 1 through 80. A player buys a ticket for $1 and marks one number on it (from

Algebra ->  Probability-and-statistics -> SOLUTION: How do you solve: In one version of the game keno, the house has a pot containing 80 balls, numbered 1 through 80. A player buys a ticket for $1 and marks one number on it (from      Log On


   

Question 369821: How do you solve:
In one version of the game keno, the house has a pot containing 80 balls, numbered 1 through 80. A player buys a ticket for $1 and marks one number on it (from 1 to 80). The house then selects 20 of the 80 numbers at random. If the number selected by the player is among the 20 selected by the management, the player is paid $3.20. Find the expected net winnings for this game.
Thank you!
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Either the player's number is in the winning twenty or not. The probability that a player's number is included in the winning twenty is C(80,19)/C(80,20) = 20/61. The probability that his number is not is 1 - C(80,19)/C(80,20) = 41/61.
If he wins, he profits $3.20 - $1 = $2.20. Otherwise his earning is $0 - $1 = -1$ (he loses!) The expected winning for playing this game is thus 2.20%2A%2820%2F61%29+%2B+%28-1%29%2A%2841%2F61%29+=+44%2F61+-+41%2F61+=+3%2F61+=+0.04918, to 5 decimal places, or virtually 5 cents!