Question

Let E and F be two events within sample space S.  Given P(E) = .7 and P(F) = .4, are the events E and F mutually exclusive? Explain why or why not.

Answer 1

Solution:

Given: E and F be two events within sample space S.

P(E) = 0.7 and P(F) = 0.4,

Events E and F are mutually exclusive if :

using addition rule of probability:

Since total probability is 1

then P( E U F) can have maximum value 1

thus

Since , events E and F are not mutually exclusive.