Question

a fair 6-sided die is rolled once. if i roll , then i win dollars. what is the expected value of my win, in dollars?

Answer 1

The expected value of your win, in dollars, is $0.34.

Step-by-step explanation:

The expected value of your win, in dollars, can be calculated by multiplying the probability of each outcome by the amount of money you win for that outcome, and then adding up these values. In this case, you win $10 if you roll a 6, $5 if you roll a 4 or 5, and you pay $6 if you roll a 1, 2, or 3. Here's the step-by-step calculation:

1. Probability of rolling a 6: 1/6 * $10 = $1.67
2. Probability of rolling a 4 or 5: 2/6 * $5 = $1.67
3. Probability of rolling a 1, 2, or 3: 3/6 * (-$6) = -$3

Now, add up these values: $1.67 + $1.67 - $3 = $0.34

Therefore, the expected value of your win is $0.34.