Question

74. A friend devises a game that is played by rolling a single six-sided die once. If you roll a 6, he pays you $3; if you roll a 5, he pays you nothing; if you roll a number less than 5, you pay him $1. Compute the expected value for this game. Should you play this game

Answer 1

Answer:

The expected value is -$0.17

Since it gives a negative expected value, the game is not favorable and should not be played

Step-by-step explanation:

Here, we want to calculate the expected game value and decide if the game is worth playing

Probability of rolling a six is 1/6

Probability of rolling a 5 is 1/6

Probability of rolling a number less than 5 is 4/6 = 2/3

So the only way to win is rolling a six

The expected value is thus;

1/6(3) - 0(1/6) - 2/3(1)

= 1/2 - 2/3

= -$0.17

Since the game gives a negative expected value, it is not favorable and should not be played