Question

Special six-sided die is made in which 1 sides have 6 spots, 2

sides have 4
spots, and 3 side has 1 spot. If the die is rolled, find the
expected value of the
number of spots that will occur.

Answer 1

To find the expected value of the number of spots that will occur when rolling the special six-sided die, we need to calculate the weighted average of the possible outcomes. The expected value is approximately 2.8333.

Step-by-step explanation:

To find the expected value of the number of spots that will occur when rolling the special six-sided die, we need to calculate the weighted average of the possible outcomes. We can do this by multiplying each outcome by its probability and then summing them up.

Let's calculate the expected value:

1. Probability of rolling 6: P(6) = 1/6
2. Probability of rolling 4: P(4) = 2/6 = 1/3
3. Probability of rolling 1: P(1) = 3/6 = 1/2

Expected value = (6 * 1/6) + (4 * 1/3) + (1 * 1/2) = 1 + 4/3 + 1/2 = 2.8333

Therefore, the expected value of the number of spots that will occur is approximately 2.8333.

Answer 2

The expected value of the number of spots on the special die is approximately 2.833. This is found by multiplying the number of spots by their respective probabilities and summing those products.

Step-by-step explanation:

The problem asks us to find the expected value of the number of spots that will appear on a special six-sided die with a non-standard distribution of spots on its sides. To calculate this, we use the formula for expected value (E(X)) which is the sum of each outcome multiplied by its probability.

In this die, 1 side has 6 spots, 2 sides have 4 spots, and 3 sides have 1 spot. The probabilities are then 1/6 for landing on the side with 6 spots, 2/6 (or 1/3) for landing on a side with 4 spots, and 3/6 (or 1/2) for landing on a side with 1 spot. We multiply each outcome by its probability and sum these products:

• E(X) = (1/6)*6 + (1/3)*4 + (1/2)*1
• E(X) = 1 + (4/3) + (1/2)
• E(X) = 1 + 1.333 + 0.5
• E(X) = 2.833

Therefore, the expected value of the number of spots is approximately 2.833. This is the average number of spots you would expect to see over a large number of rolls of the die.