Question

An ordinary (falr) dle is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a dle 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 divisible by 5.
Write your answers as fractions.
(a) P(X) =

(b) P(B) =

Answer 1

By finding the number of outcomes that meet each criteria, we will see that the probabilities are:

• A) P = 0.25
• B) P = 7/36 = 0.194

How to find the probability?

We know that the fair die has 6 outcomes, so if we roll it twice, there are a total of:

6*6 = 36 outcomes.

To find the probability of getting a given event, we need to find the number of outcomes that make the event true.

A) The sum is greater than 8.

The outcomes that make this true are:

first roll    second roll     sum

 4                   5                 9

 4                   6                 10

5                     5                10

5                    6                 11

6                     3                 9

6                    4                 10

6                     5                11

6                     6                  12

3                     6                   9

So there are 9 outcomes whose sum is greater than 8, so the probability to getting this event is:

P = 9/36 = 0.25

B) The sum is divisible by 5.

The sum must be 5 or 10, the outcomes that give that are:

first roll    second roll     sum

   1                   4                 5

   2                  3                 5

   3                  2                 5

   1                   4                 5

   4                   6                10

  5                    5                10

   6                   4                 10

There are 7 outcomes, so the probability is:

P = 7/36 = 0.194

If you want to learn more about probability, you can read:

brainly.com/question/251701