Question

Suppose that you are offered the following "deal." You roll a six-sided die. If you roll a 6 , you win $10. If you roll a 3,4 or 5 , you win $1. Otherwise, you pay $3. Complete the Probability Distribution table shown below. Let X represent your profit and list the X values from smallest to largest. Round to 4 decimal places where appropriate. Probability nictrihution Table Find the expected profit. $ (Round to the nearest cent)

Answer 1

The question pertains to constructing a probability distribution table for a game involving rolling a six-sided die and calculating the expected profit. The random variable X represents the profit, with possible values of $10, $1, and -$3, associated with the respective outcomes of the die roll.

Step-by-step explanation:

The student is asked to complete a probability distribution table and find the expected profit from a game involving rolling a six-sided die with various outcomes tied to monetary gains or losses.

Probability Distribution and Expected Profit

For rolling a die:

• If you roll a 6, you win $10.
• If you roll a 3, 4, or 5, you win $1.
• If you roll a 1 or 2, you pay $3.

The random variable X represents your profit from the game, which can take on the values of $10, $1, and -$3 with their respective probabilities based on the possible outcomes of rolling the die.

Constructing the Table

For the probability distribution table, consider the following values:

• X = $10, this occurs with a probability of 1/6 when you roll a 6.
• X = $1, this occurs with a probability of 3/6 (or 1/2) when you roll a 3, 4, or 5.
• X = -$3, this occurs with a probability of 2/6 (or 1/3) when you roll a 1 or 2.

The expected profit is calculated by multiplying each outcome by its probability and summing these products. The answer will be the average amount you can expect to win or lose per game when playing a large number of times.