Question from the 'GMAT Review 12th ed'

bmaree wrote:
P(B or C)= P(B)+P(C)-P(B)P(C) by independence
=0.40+0.85 = 0.91

That last line should read:

=0.40+0.85 - (0.40)(0.85) = 0.91

bmaree wrote:
Note that P(A or C) and P(A and C) cannot be determined using the information given[/color] [I assume that's because the question didn't state whether they're mutually exclusive or independent in relevance to each other]
But it can be determined that A and C are not mutually exclusive since P(A)+P(C)=1.08, which is greater than 1, and therefore cannot equal P(A or C); from this it follows that P(A and C)>= 0.08. [How did they reach this conclusion? where did the 0.08 come from?]

If A and C were mutually exclusive, then P(A or C) would be equal to P(A) + P(C), so would be equal to 0.23 + 0.85 = 1.08. But that's greater than 1, and probabilities can never be greater than 1. So, since we get a nonsensical answer if we assume A and C are mutually exclusive, it must be impossible that A and C are mutually exclusive. Finally the 0.08 comes from the following: P(A or C) = P(A) + P(C) - P(A and C). We know that P(A or C) must be at most 1. Since P(A) + P(C) is 1.08, then to bring the right side of that equation down to a value of at most 1, it must be that P(A and C) is at least 0.08.

All of that said, I'd strongly recommend *not* using the OG to review counting and probability principles. Their treatment of the subject is pedantically formal and abstract. It's neither easy to follow, nor easy to apply to actual test questions. In general, the practice questions in the OG are great, but the review material at the beginning leaves a lot to be desired.