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 7 Event B: The sum is an even numberWrite your answer as fractions

Answer 1

EVENT A.

We have to count in how many possible ways does the sum of the two rolls of the die add up to more than 7. The possibilities are:

6+2

6+3

6+4

6+5

6+6

5+3

5+4

5+5

5+6

4+4

4+5

4+6

3+5

3+6

2+6

Then, there is 15 ways that the sum os greater than 7. Now we have to calculate how many combinations there is in total, which is 6 possible outcomes for the first roll and other 6 for the second roll, then there is 6x6=36 possible outcomes.

The probability for event A is then 15/36 or 5/12

EVENT B:

In a similar way, we have to count how many ways there is such that the sum is even:

1+1

1+3

1+5

2+2

2+4

2+6

3+1

3+3

3+5

....

We notice that there is 3 ways for each number from the first roll. Then the total is 6*3=18 ways such that the sum is even. The total possible outomes is 6x6=36.

Hence the probability for Evenet B is 18/36 or 1/2