Question

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.

Answer 1

Answer:

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