A certain game consist of rolling a single fair die and based off as a following numbers listed in the picture

Given:

A fair die is rolled.

It pays off $10 for 6, $7 for a 5, $4  for a 4 and no payoff otherwise.

To find:

The expected winning for this game.

Solution:

If a die is rolled then the possible outcomes are 1, 2, 3, 4, 5, 6.

The probability of getting a 6 is:

The probability of getting a 5 is:

The probability of getting a 4 is:

The probability of getting other numbers (1,2,3) is:

We need to find the sum of product of payoff and their corresponding probabilities to find the expected winning for this game.

Therefore, the expected winnings for this game are $3.50.

step-by-step explanation:

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