Probability - Mutually exclusive

[cait88]

If anyone could help me with a few probability problems, that would be awesome.

Suppose B and C are events with P(B)=1/4, P(C)=1/3 and P(B or C)=1/2. Are B and C mutually exclusive? Find P(B and C).

I know that if the events are mutually exclusive, P(B and C)=0
But I don't know how to prove that.

Thanks

 

[pka]

\(\displaystyle \begin{array}{rcl}
P(B \cup C) & = & P(B) + P(C) - P(B \cap C) \\
\frac{1}{2} & = & \frac{1}{4} + \frac{1}{3} - P(B \cap C) \\
P(B \cap C) & = & \frac{1}{{12}} \\
\end{array}\)

Are they exclusive?

 

[cait88]

No? Because it doesn't equal 0.

 

[pka]

RIGHT!

 

[cait88]

Thanks so much!