A fair die is rolled and the sample space is given S={1,2,3,4,5,6}. Let A={1,2} and B={3,4}. Which of the following statements is true?

a. A and B are mutually exclusive

b. P (A or B) = 4/6.

c. P (A or B) = P (A) + P (B).

d. All of the choices are correct.

d

Step-by-step explanation:

The given sample space S is

S={1,2,3,4,5,6}

The given event A and event B are

A={1,2} and B={3,4}.

As A and B have nothing in common i. e. A∩B={} thus, A and B are mutually exclusive.

As A and B are mutually exclusive then P (A or B) can be calculated as

P (A or B) = P (A) + P (B) - P (A∩B)

We know that if A and B are mutually exclusive events then P (A∩B) = 0. So,

P (A or B) = P (A) + P (B)

In the given scenario

P (A) = n (A) / n (S) = 2/6 and

P (B) = n (B) / n (S) = 2/6

P (A or B) = 2/6+2/6=4/6

P (A or B) = 4/6

So, all the choices are correct