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 divisible by
2
.
Round your answers to at least two decimal places.

To compute the probability of each event, we first need to determine the total number of possible outcomes and the number of favorable outcomes for each event.

For Event A: The sum is greater than 7.
To find the favorable outcomes, we need to consider all the combinations of the dice rolls that result in a sum greater than 7. These combinations are:
- (2, 6)
- (3, 5)
- (3, 6)
- (4, 4)
- (4, 5)
- (4, 6)
- (5, 3)
- (5, 4)
- (5, 5)
- (5, 6)
- (6, 2)
- (6, 3)
- (6, 4)
- (6, 5)
- (6, 6)

There are 15 favorable outcomes for Event A.

Since each die has 6 sides, the total number of possible outcomes is found by multiplying the number of sides of one die by the number of sides of the other die. Therefore, there are 6 * 6 = 36 possible outcomes.

The probability of Event A is given by the favorable outcomes divided by the total number of possible outcomes:
P(A) = favorable outcomes / total outcomes
P(A) = 15 / 36
P(A) ≈ 0.42

For Event B: The sum is divisible by 2.
To find the favorable outcomes, we need to consider all the combinations of the dice rolls that result in a sum divisible by 2. These combinations are:
- (1, 1)
- (1, 3)
- (1, 5)
- (2, 2)
- (2, 4)
- (2, 6)
- (3, 1)
- (3, 3)
- (3, 5)
- (4, 2)
- (4, 4)
- (4, 6)
- (5, 1)
- (5, 3)
- (5, 5)
- (6, 2)
- (6, 4)
- (6, 6)

There are 18 favorable outcomes for Event B.

Using the same reasoning as above, there are 36 possible outcomes.

The probability of Event B is given by the favorable outcomes divided by the total number of possible outcomes:
P(B) = favorable outcomes / total outcomes
P(B) = 18 / 36
P(B) = 0.5

Therefore, the probability of Event A is approximately 0.42, and the probability of Event B is 0.5.

draw a table of 6 rows and 6 columns, with the entries being the sums of the row and column count

e.g.
/// 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 10 11
6

Now count the "sums" that related to your question
and you should be able to answer all of these.
remember your probability is .... /36