A bag has 8 red tiles and 2 green tiles. In a charity carnival game, you pay $5 to randomly pull a tile from the bag. The payout for pulling a red tile is $1 and the payout for pulling a green tile is $10. Which of the followig are true or false.

a. The expected payoff per game for the charity is $2.20.
b. In 20 games, the charity can expect to make $44.
c. In 30 games, the charity can expect to make $120.
d. In 5 games, the player can expect to lose $11.

B is true as a bag of 8 red tiles and 2 green tiles you pay 5 per tile meaning in twenty games you pay $100(50 per bag) and the total amount you win back is $56(28 per bag) so the equation would be $100 - $56= $44 profit to the charity

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aroranishant799 aroranishant799 · Answer 2 · 2022-05-21T22:44:52+02:00

Hence only statement 1 is correct,∴The expected payoff per game for the charity is $2.20.

What is payoff?

Money provided to someone as a bribe, reward, or when they leave a position. As a result, a mathematical function representing the award awarded to a single player at the game's conclusion has been developed.

How to Solve?

Given a bag of tiles containing 8 red tiles, 2 green tiles.

Probability of drawing a red tile =1/8

Probability of drawing a green tile =1/2

If red tile is pulled payout is $1 else $10

Payout=

payout for 1 game= $1*8/10+$10*2/10-$5=2.20

payout in 20 games =$1*10*8/10+$10*10*2/10-$5*20=-72

payout for 30 games=$1*15*8/10+$10*15*2/10-$5*30=0

payout in 5 games=$1*5*8/10+10*5*2/10-$5*5=$25

Hence only statement 1 is correct, ∴The expected payoff per game for the charity is $2.20.

Learn more about probability https://brainly.com/question/14211455

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