Question

Consider the sample space of single-digit integers

S= 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

And let

A= 2, 4, 6, 8

B= 1, 3, 5, 7, 9

C= 0, 1, 2, 3

A) Are events A and B mutually exclusive?

B) Are events A and C mutually exclusive?

Answer 1

Solution:

Two sets A and B are said to be mutually exclusive if their intersection is zero.

i.e. A B is a null set.

i.e. There is no any common element in the sets.

A)

From given sets , we can say that there is no any common element in A and B

i.e. A B is a null set.

YES , events A and B are mutually exclusive

B)

From given sets ,

A C = { 2 }

i.e. A C is not a null set.

NO , events A and C are NOT mutually exclusive.