Question

At a carnival, you pay $5 to roll two fair six-sided dice, each numbered 1 - 6. If your roll contains a 1, you win $1. If your roll sums to a number greater than 8, you win $10. Let the random variable X denote your net winnings.

(a) Draw the probability distribution of X.
(b) What are your expected net winnings (to the nearest cent)?

Answer 1

To draw the probability distribution of X, we need to consider all the possible outcomes and their respective probabilities. The expected net winnings (to the nearest cent) is -$0.14.

Step-by-step explanation:

To draw the probability distribution of X, we need to consider all the possible outcomes and their respective probabilities. Let's list all the possible values of X and their probabilities:

X = -5 with probability 10/36

X = -4 with probability 10/36

X = -3 with probability 10/36

X = -2 with probability 10/36

X = -1 with probability 10/36

X = 0 with probability 6/36

X = 1 with probability 2/36

X = 5 with probability 2/36

X = 10 with probability 2/36

Next, to find the expected net winnings, we multiply each value of X by its respective probability and sum the products. The expected net winnings is calculated as follows:

-5 * (10/36) + -4 * (10/36) + -3 * (10/36) + -2 * (10/36) + -1 * (10/36) + 0 * (6/36) + 1 * (2/36) + 5 * (2/36) + 10 * (2/36) = -0.14

Therefore, the expected net winnings (to the nearest cent) is -$0.14.