SOLUTION: 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?

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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): You can put this solution on YOUR website!


C and D cannot be mutually exclusive since P(C|D) is not equal to zero.


John

My calculator said it, I believe it, that settles it


I > Ø
Answer by ikleyn(52898)   (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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