## probability Q.

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### probability Q.

by godemol » Sun Aug 09, 2009 9:29 pm
Guys, a simple question, but I am having hard time grasping. Need your help:

The events A and B are independent. The probability that event A occurs is p and the probability that event B occurs is q. Which of the following is equal to the probability that exactly one of the events A and B occurs?

A. p &#8722; 2pq
B. q &#8722; pq
C. p + q &#8722; 2pq
D. p + q &#8722; pq
E. p + q

The answer is C. But, the part that I am having trouble understanding is the bold statement above: the probability that exactly one of the events A and B occurs...isn't that equivalent to "the probability that either A or B occurs? In other words, P(A or B), which would make choice D a correct answer?

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by tohellandback » Sun Aug 09, 2009 9:41 pm
the probability that exactly one of the events A and B occurs?
A occurs and B does not occur= p(1-q)

or, B occurs and A does not occur=q(1-p)

take the sum = p-pq+q-pq
=p+q-2pq