Question

# Suppose you are playing a game of chance. You pay \$50 to play by rolling a...

1. Suppose you are playing a game of chance. You pay \$50 to play by rolling a fair die one time, if you roll a 1 you will receive \$300, if you roll a 3 or a 6 you will receive \$150, if you roll a 2, 4 or 5 you will receive nothing.                                                         (6)
1. Find your (the player’s) expected value for this game of chance.
1. Based on this expected value, do you think this would be a good game to play? Why or why not?

P(rolling 1) = 1/6, gain = 300 -50 = 250

P(rolling 3 or 6) = 2/6 ; gain = 150 - 50 = 100

P(rolling 2,4 or 5) = 3/6 ; loss = -50

 Rolling Gain/ loss P(x) x* P(x) 1 250 0.167 41.667 3 or 6 100 0.333 33.333 2,4 or 5 -50 0.50 -25 Total Total 1.00 50.000

E(X) = X * P(X) = (250 * 0.167) + (100 * 0.333) + (-50 * 0.50) = 50

a. Expected value for the game = \$ 50

b. This would be a good game to play as the expected value of winning is \$50. So there are chances of winning and receiving money.