Answer to Question #155122 in Economics for maryam

Question

a game is played with 10$ .in the game ,the ball dropped from the top falls through one of the 7 holes below.if the person correctly predicts the hole where the ball will fall , he\she earns 30$.which hole has a higher chance and what is the probability ? what is the expected profit of the person from a game ? what would be the expected profit if the person choose the 3th hole from the left(hole c)?

Answer 1

The probability tree is (in %):

                  50 50

                25 50 25

           12.5 37.5 37.5 12.5

         6.25  25  37.5  25  6.25

3.125 15.625 31.25 31.25 15.625 3.125

1.5625 9.375 23.4375 31.25 23.4375 9.375 1.5625

The middle hole d has a higher chance with the probability 0.3125 or 31.25%. The expected profit of the person from a game depends on his choise but in average it is 30/7 - 10 = -5.71.

The expected profit if the person choose the 3th hole from the left (hole c) is: 0.234375×30 - 10 = -2.97.