Let A and B be the events such that and P(not A or not B)

State whether A and B are

(i) mutually exclusive

(ii) independent

Given: A and B are the events such that P(A) = and P(B) = and

P(not A or not B) =

To Find: i)If A and B are mutually exclusive

Since P(not A or not B) = i.e., P() =

we know that , P() = P(AB)’= 1- P(AB) =

P(AB) = 1- = Equation 1

Since for two mutually exclusive events P(AB) = 0

But here P(AB) 0

Therefore , A and B are not mutually exclusive.

ii)If A and B are independent

The condition for two events to be independent is given by

P(E₁ E₂) = P(E₁) P(E₂)

=

= Equation 2

Since Equation 1 Equation 2

A and B are not independent