Question 1167002: Consider the following scenario:
• Let P(C) = 0.5
• Let P(D) = 0.6
• Let P(C | D) = 0.7
Are C and D mutually exclusive? Why or why not?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source):
Answer by ikleyn(52887)  (Show Source):
You can put this solution on YOUR website! .
Tutor @solver91311 just gave you the correct answer.
I also want to add my 2 cents.
The condition P(C|D) = 0.7 just tells you that the events C and D are not mutually exclusive.
Otherwise, P(C|D) would be zero, by the definition of mutually exclusive events.
But, actually, this condition P(C|D) = 0.7 is EXCESSIVE.
Two conditions, P(C) = 0.5 and P(D) = 0.6 are just ENOUGH to conclude that the the events C and D are not mutually exclusive.
Indeed, otherwise it would be
P(C U D) = P(C) + P(D) = 0.5 + 0.6 = 1.1 > 1 (for mutually exclusive events, probabilities are added (!) )
which is IMPOSSIBLE.
So, again, having two conditions P(C) = 0.5 and P(D) = 0.6 is just enough to conclude
that the events C and D ARE NOT mutually exclusive.
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