### CFA Practice Question

There are 410 practice questions for this study session.

### CFA Practice Question

Of letters sent through a certain post office, 20% have insufficient postage, 48% have the wrong zip code, and 58% have one or both of these problems. What is the probability that a letter has both insufficient postage and the wrong zip code?
A. 0.10
B. 0.30
C. 0.68
Explanation: Let A denote the event that the letter has insufficient postage and B denote the event that it has the wrong zip code. We know that P(A) = 0.20, P(B) = 0.48 and P(A or B) = 0.58. Solving using the general rule of addition for P(A and B), one obtains P(A and B) = P(A) + P(B) - P(A or B). Thus, the probability of a letter having both problems is P(A and B) = 0.20 + 0.48 - 0.58 = 0.10.

User Comment
nostalgia Can anyone clarify this? If 58% have either one OR BOTH these problems, it doesn't sound like P(A or B) = 58%. It should be P(A or B) + P(AB) = 58%.
kamcooler Think like this: Only A + Only B + Both = 58

Only A = 20 - Both
Only B = 48 - Both

Substitute into original: (20 - Both) + (48 - Both) + Both = 58

Solve for Both...
linzlinked The questions is asking P(A and B)=?, but the equation above for P(AandB)=0.2+0.48-0.58=0.1 is for P (A or B), isn't it? I thought P (A and B) = P(A)*P(B) for 2 independent probabilities. Anybody can help clarify a bit? Thanks
tferik My short cut thinking
-If 20% has insufficient postage
-The question asks for both insufficient postage and wrong zip
-Therefore, the answer must be less than 20% because not all insufficient postage will have an incorrect zip
-Of course, if there are other answer choices on the real exam, then, further work will be needed, but at least it can help eliminate a choice