If a die is rolled twice, what is the probability of rolling a 5 and then a 2?

Solution:

Given, a die is rolled twice

We have to find the probability of rolling a 5 and then a 2.

When a die is rolled twice, we get one of the following combinations:

1, 1 - 1, 2 - 1, 3 - 1, 4 - 1, 5 - 1, 6

2, 1 - 2, 2 - 2, 3 - 2, 4 - 2, 5 - 2, 6

3, 1 - 3, 2 - 3, 3 - 3, 4 - 3, 5 - 3, 6

4, 1 - 4, 2 - 4, 3 - 4, 4 - 4, 5 - 4, 6

5, 1 - 5, 2 - 5, 3 - 5, 4 - 5, 5 - 5, 6

6, 1 - 6, 2 - 6, 3 - 6, 4 - 6, 5 - 6, 6

Total number of combinations in the sample space = 36

5, 2 appears only once in the above list of possible combinations.

2, 5 cannot be considered.

P(5 and 2) = 1/36

Therefore, the probability of rolling a 5 and then a 2 is 1/36.

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If a die is rolled twice, what is the probability of rolling a 5 and then a 2?

Summary:

If a die is rolled twice, the probability of rolling a 5 and then a 2 is 1/36.