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.Kate is considering whether to play the second game.If Kate only cares about the expected value of the outcome and does not care about risk,she should:
A) not play since she never wins anything.
B) play if the cost of playing the game is greater than the expected value of the payoff.
C) compare the cost of playing the game with the value of her time.
D) play if the cost of playing the game is less than the expected value of the payoff.

Question

Quizplus · Accepted Answer

Kate should play the second game because it has a higher expected value than the first game. The expected value of the second game is (1/10)($20) + (4/10)($5) + (5/10)($1) = $2.9, while the expected value of the first game is (1/4)($20) + (3/4)($1) = $5.25. Thus, if Kate only cares about the expected value and not the risk involved, she should choose the second game. Option A is incorrect because Kate can win in the second game. Option B is incorrect because the cost of playing the game is fixed at $5. Option C is irrelevant as the problem only considers the expected value of the outcome.

Suppose Jack and Kate Are at the Town Fair and Are