If two events A and B are mutually exclusive then PrA B Pr

If two events A and B are mutually exclusive, then Pr(A ? B) = Pr(A) x Pr(B). True or False. Explain

Solution

True

If events A and B in a sample space S
are Mutually Exclusive, then :

P( A ? B ) = 0.
______________________________

Hence, by Addition Thm of Probability,
which states : P(AUB) = P(A) + P(B) - P(A?B),
we get :

P(A U B ) = P(A) + P(B).
_______________________________

Also, by Multiplication Thm of Probability,
P(A/B) = P(A?B) / P(B) = 0/P(B) = 0.
Similarly, P(B/A) = 0.
Thus, if A and B are Mutually Exclusive, then

P(A/B) = 0 = P(B/A).
_______________________________

If A and B are Mutually Exclusive,
then the occurrence of any one of them
prevents the other from happening, i.e.,
the occurrence of each of them depends
upon the other.

Hence, two mutually exclusive events can
never be independent.
They are always Dependent.