An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (repr

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

5

.
Event

B

: The sum is not divisible by

4

.

Explanation / Answer

Dear Student Thank you for using Chegg !! Given that a dice is rolled twice Hence the total number of possibilities = 6*6 = 36 outcomes with sum less than or equal to 5 1 1 1 2 1 3 1 4 2 1 2 2 2 3 3 1 3 2 4 1 => Number of outcomes with sum < 5 = 10 => Number of outcomes with sum > 5 = 36-10 = 26 Probability = 26/36 = 0.72222222 Event B Outcome with Sum is divisible by 4 i.e. sum is 4, 8 ,12 1 3 3 1 2 2 2 6 3 5 4 4 5 3 6 2 6 6 => Number of outcomes with sum divisible by 4 is 9 => Number of outcomes with sum not divisible by 4 is 36 - 9 = 27 Probability that sum is not divisible by 4 is = 27/36 = 0.75 Solution

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