# Only one of two events occurs

#### Hans Rudel

##### New Member
P(A) = 8/15
P(B) = 1/3
P(A|B) = 1/5

(Question) calculate the probability that only one event occurs.

i have already calculated that the P(A&B) = P(B) x P(A|B) = 1/15

P(A'&B') = 0.2 from the following

P(AorB) = (P(A) + P(B) - (PA&B)
so
1 - P(AorB) = P(A'&B')

i thought the answer to the question would be (P(A') x P(B)) + (P(A) x P(B')) but that doesnt work.

Note: the answer is suppose to be 11/15

I would really appreciate any help on this.

#### vinux

##### Dark Knight
Hint: only one event occurs => A'&B or A&B'
Draw the ven diagram and visualise the problem may help

#### Hans Rudel

##### New Member
Hi Vinux, thanks for replying to my problem. I have managed to solve it both with the following relationship and the Venn diagram as u mentioned. I had forgotten that P(A&B') was just the section of P(A) excluding the joint events.

P(A) = P(A&B) + P(A&B')

i have the created a Venn diagram if anyone is interested. Thanks again for your help.