ankur.agrawal wrote: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 after some discussion.
Hi!
Some tricky working in (1) which we need to carefully translate, but once we do it's clear that each statement is sufficient alone.
Q: What's the probability that Memphis isn't chosen to host?
First, we need to recognize that if we can answer "what's the probability that Memphis IS chosen to host?" we can also answer the original question, since:
Chance not chosen = 1 - Chance chosen.
Realizing that makes us quickly see that (2) is sufficient alone: eliminate (A), (C) and (E).
Now let's look at (1):
(1) The probability that
any one of the 8 cities does not win the competition is 7/8. (Emphasis mine.)
The only way that the probability of any one city not winning could be 7/8 is if each city has exactly the same chance of winning. Since there are 8 cities, each must have a 1/8 chance to win. Now that we know that Memphis has a 1/8 chance to win, we can answer the original question.
Of course, as soon as you realize that (1) means that each city has a 7/8 chance of losing, you can directly conclude that Memphis, one of the cities, has a 7/8 chance of losing - we didn't really need to calculate the chance of Memphis winning to identify (1) as sufficient.
(1) and (2) are each sufficient alone: choose (D).
