a fair (6 sided) die is rolled TWO times. What is the probability that the first die is a 2 or the second die is a prime

The probability that the first die is a 2 or the second die is a prime = 1/12

Step-by-step explanation:

It is given that, a fair (6 sided) die is rolled TWO times.

The sample space for rolling 2 dies

(1, 1), (1, 2) ... (1,6)

(2,1) ...

.

.

(6, 1) ... (6, 6)

There are total of 6^2 = 36 sample space

To find the probability

The prime numbers from 1 to 6 are 2, 3 and 5

the possible outcomes are (2,1), (2, 3) and (2, 5)

The probability that the first die is a 2 or the second die is a prime = 3/36 = 1/12