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.If Jack only cares about expected value,and not risk,he should decide to play a game if:
A) the expected value of the payoff is higher than the price to play the game.
B) the expected value of the payoff is lower than the price to play the game.
C) the expected value of the payoff is higher than the expected value of the payoff in the other game.
D) the expected value of the payoff is double the price to play the game.

Question

Quizplus · Accepted Answer

Jack should play a game if the expected value of the payoff is higher than the price to play the game. 
For the first game, the expected value of the payoff is (1/4)⋅$20 + (3/4)⋅$1 = $5 (calculated by multiplying each outcome by its probability and summing them up), which is higher than the price to play the game ($5). 
For the second game, the expected value of the payoff is (1/10)⋅$20 + (4/10)⋅$5 + (5/10)⋅$1 = $3.5, which is lower than the price to play the game ($5). 
Therefore, Jack should choose to play the first game.

Suppose Jack and Kate Are at the Town Fair and Are