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.
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.
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