Question

A coin is flipped and a 6-sided die is rolled. If you flip a tails and an even number you get $4. If you flip a tails and an odd number you pay $1. If you flip a heads and a number less than 3 you get $A and if you flip a heads with any other number you pay $6. What is the expected value? How much do you win lose if you play this game? Round to the nearest cent if needed.​

Answer 1

The expected value of the game is -$0.62, indicating an expected average loss per game. Playing this game would result in losing $0.62, on average.

Step-by-step explanation:

To find the expected value, we need to multiply each outcome by its probability and sum up the results. Let's calculate:

• If you flip a tails and an even number, you get $4. The probability of this happening is 0.5 * (1/3) = 0.1667.
• If you flip a tails and an odd number, you pay $1. The probability of this happening is 0.5 * (2/3) = 0.3333.
• If you flip a head and a number less than 3, you get $A. The probability of this happening is 0.5 * (2/6) = 0.1667.
• If you flip a head with any other number, you pay $6. The probability of this happening is 0.5 * (4/6) = 0.3333.

We can now calculate the expected value:

(4 * 0.1667) + (-1 * 0.3333) + (A * 0.1667) + (-6 * 0.3333)

Since we don't have a specific value for $A, we can't calculate the exact expected value. However, we can determine how much you would win or lose on average. If you play this game repeatedly, over a long string of games, you would expect to lose $0.62 per game, on average. Therefore, you should not play this game to win money.