A certain game consists of rolling a single fair die and pays off as follows: $5 for a 6, $3 for a 5, 51 for a 4, and no payoff otherwise. Find the expected winnings for this game.

The expected winning is + $2.17

Step-by-step explanation:

Here, we want to calculate the expected winnings for the game

The number of possible results are;

1,2,3,4,5,6

Probability of each value is 1/6

So expected pay off is as follows;

1/6(5) + 1/6(3) + 1/6(5) + 0

= 5/6 + 3/6 + 5/6

= 5/6 + 5/6 + 1/2 + 0

= 10/6 + 1/2 = 5/3 + 1/2 = (10 + 3)/6 = 13/6 = 2.1667