Question

Greta rolls a pair of 6- sided dice. If she gets two of a kind, she scores the sum of the 2 dice. Otherwise, she gets 0 points. What is the expected value of the number of points she scores on a toss of the 2 dice?

Answer 1

The expected value of the number of points Greta scores on a toss of the two dice is 3.5 points.

Step-by-step explanation:

The expected value of the number of points Greta scores on a toss of the two dice can be calculated by finding the probability of each outcome and multiplying it by the corresponding score. Since there are 6 possible outcomes on each die, the total number of outcomes in the sample space is 6 * 6 = 36.

There are 6 outcomes where Greta gets two of a kind: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). The sum of these outcomes is 1 + 2 + 3 + 4 + 5 + 6 = 21. Therefore, the probability of getting two of a kind is 6/36 = 1/6.

For the remaining outcomes where Greta does not get two of a kind, she scores 0 points. The probability of this happening is 1 - 1/6 = 5/6.

To calculate the expected value, we multiply the probability of each outcome by its score and sum them up:

Expected value = (1/6 * 21) + (5/6 * 0) = 21/6 = 3.5 points.