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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 not divisible by 4. Write your answers as fractions.

Answer 1

Hi This problem is asking about probability.

Given a die that is rolled twice. What is the probability

Event A: The sum is greater than 8 .

Event B : The sum is not divisible by 4.

Write your answers as fractions.

We can make a table of the possible outcomes of rolling the die 2 times

The left side represents the first roll (Possible numbers are 1 through 6)

The top represent the 2nd roll (again Possible numbers are 1 through 6)

The table will be the total of the 2 numbers

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

Probability = (Number of Favorable outcomes) / (Number of Possible Outcomes)

For Event A, The sum is greater than 8

There are 10 outcomes that are greater than 8.

There are a total of 36 possible outcomes.

The probability of Event A = 10 / 36 Simplified is 5/18

Event B : The sum is not divisible by 4. The outcomes divisible by 4 would be when the die total to 4,8,or 12

There are 27 outcomes that are NOT divisible by 4

The probability of Even B = 27/36 Simplified is 3/4

Let me know if you have more questions....