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