Question

An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.

Compute the probability of each of the following events.
Event A: The sum is greater than 8.
Event B: The sum is an even number.
Write your answers as fractions.

Answer 1

Explanation:

There are 6 possible outcomes for each of the two rolls, so there are 6 x 6 = 36 possible outcomes for the sum of two rolls.

Event A: The sum is greater than 8.

There are five possible ways to achieve a sum greater than 8: (3, 6), (4, 5), (4, 6), (5, 4), and (6, 3). Each of these outcomes has a probability of 1/36. Therefore, the probability of event A is:

P(A) = 5/36

Event B: The sum is an even number.

There are three possible ways to achieve an even sum: (1, 1), (2, 2), and (3, 3). Each of these outcomes has a probability of 1/36. There are also three possible ways to achieve a sum of 4: (1, 3), (2, 2), and (3, 1). Each of these outcomes has a probability of 1/36. Similarly, there are three possible ways to achieve a sum of 6, 8, 10, and 12. Therefore, the probability of event B is:

P(B) = (3 + 3 + 3 + 3 + 3 + 3)/36

P(B) = 18/36

P(B) = 1/2

Therefore, the probability of event A is 5/36 and the probability of event B is 1/2.