Problem:
The probability that event A occurs is 43; the probability that event B occurs is 32. Let p be the probability that both A and B occur. The smallest interval necessarily containing p is the interval
Answer Choices:
A. [121,21]
B. [125,21]
C. [21,32]
D. [125,32]
E. [121,32]
Solution:
Let P(E) be the probability that event E occurs. By the Inclusion-Exclusion Principle, P(A∪B)=P(A)+P(B)−P(A∩B). So p=P(A∩B)=P(A)+P(B)−P(A∪B)=43+32−P(A∪B).
At the most, P(A∪B)=1; at the least, P(A∪B)= max{P(A),P(B)}=43. So 43+32−1≤p≤43+32−43, which is (D).
(Note: only if A and B are independent is p=1/2.)