BTGmoderatorDC wrote: ↑

Thu Mar 04, 2021 5:32 pm

8 cities, including Memphis, are finalists to be chosen to host a political convention. Exactly one city will be chosen to host the convention. What is the probability that Memphis is not chosen?

(1) The probability that any one of the 8 cities does not win the competition is 7/8.

(2) The probability that Memphis wins the competition is 1/8.


OA D

Source: Manhattan Prep

Target question: What is the probability that Memphis is not chosen?

ASIDE: At first glance, it may seem like we already have enough information the answer the target question. After all, if there are 8 cities, then P(Memphis is chosen) = 1/8, which means Memphis is not chosen) = 7/8, right?
Not quite. Notice that the question does NOT say that a city will be chosen at random. So, we can't assume that each city has the same chances of being selected. So, at this point (before examining the statements), we cannot answer the target question.

Statement 1: The probability that any one of the 8 cities does not win the competition is 7/8.
So, P(a particular city is not chosen) = 7/8
So, P(Memphis is not chosen) = 7/8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The probability that Memphis wins the competition is 1/8.
We can use the complement to see that P(Memphis is not chosen) = 1 - 1/8 = 7/8
So, P(Memphis is not chosen) = 7/8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent