# Probability that only event A occurs?

• Feb 18th 2010, 11:40 AM
dynas7y
Probability that only event A occurs?
Suppose there are three events, A, B, and C. You are also given the values of: P(A), P(B), P(C), P(A intersect B), P(B intersect C), P(A intersect C), and P(A intersect B intersect C). How would you find the probability that only event A occurs?
• Feb 18th 2010, 12:38 PM
Plato
Quote:

Originally Posted by dynas7y
Suppose there are three events, A, B, and C. You are also given the values of: P(A), P(B), P(C), P(A intersect B), P(B intersect C), P(A intersect C), and P(A intersect B intersect C). How would you find the probability that only event A occurs?

What you want is $P\left(AB^cC^c\right)$, probability of A and not B and not C.
I suggest you draw a Venn diagram to see this.
$P\left(AB^cC^c\right)=P(A)-P(AB)-P(AC)+P(ABC)$
• Feb 18th 2010, 01:29 PM
dynas7y
Ahh, I see. That makes a lot of sense now. Thanks a lot for the quick reply (Clapping)