Suppose Jack and Kate are at the town fair and are choosing which game to play.The first game has a bag with four marbles in it-1 red marble and 3 blue ones.The player draws one marble from the bag; if it is red,they win $20 and if it is blue,they win $1.The second game has a bag with 10 marbles in it-1 red,4 blue,and 5 green.The player draws one marble from the bag; if it is red,they win $20; if it is blue,they win $5; and if it is green,they win $1.Both games cost $5 to play.Jack is considering whether to play the first game.If Jack only cares about the expected value of the outcome and does not care about risk,he should:
A) not play the game, since it costs $5 and the expected payoff is $5.75.
B) play the game since it costs $5, and the expected payoff is $5.75.
C) play the game since it costs $5.75 and the expected payoff is $5.
D) not play the game since it costs $5.75 and the expected payoff is $5.

Question

Quizplus · Accepted Answer

To calculate the expected value of the outcome, we multiply the probability of winning each prize by the amount of the prize and add them up. 
For the first game: 
- The probability of winning $20 is 1/4 (since there is 1 red marble out of 4 total marbles) 
- The probability of winning $1 is 3/4 (since there are 3 blue marbles out of 4 total marbles) 
Expected value = (1/4)($20) + (3/4)($1) = $5.75
Since the game costs $5 to play, and the expected payoff is $5.75, Jack should play the game.

Suppose Jack and Kate Are at the Town Fair and Are