Homework SourseFind the probabilities of the following events in terms of P
Find the probabilities of the following events in terms of P[A], P[B], and P[A intersect B]:
(a) A occurs and B does not occur; B occurs and A does not occur.
(b) Exactly one of A or B occurs.
(c) Neither A nor B occurs.
Solution
(a) A occurs and B does not occur; B occurs and A does not occur.
= P(A-B)UP(B-A)
= P(A)+P(B)-2P(AB)
------------------------------------------
(b) Exactly one of A or B occurs.
= P(AB\' and BA\')
=
= P(A-B)UP(B-A)
= P(A)+P(B)-2P(AB)
-----------------------------
c) Neither A nor B occurs.
= P(AUB)c = 1-P(AUB)
= 1-P(A)-P(B)+P(AB)
![Find the probabilities of the following events in terms of P[A], P[B], and P[A intersect B]: (a) A occurs and B does not occur; B occurs and A does not occur. (](/WebImages/31/find-the-probabilities-of-the-following-events-in-terms-of-p-1088976-1761573071-0.webp "Find the probabilities of the following events in terms of P[A], P[B], and P[A intersect B]: (a) A occurs and B does not occur; B occurs and A does not occur. (")
