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# 8 cities, including Memphis, are finalists to be chosen to host a poli

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Math Expert
Joined: 02 Sep 2009
Posts: 52386
8 cities, including Memphis, are finalists to be chosen to host a poli  [#permalink]

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03 Nov 2014, 07:06
1
3
00:00

Difficulty:

5% (low)

Question Stats:

83% (00:56) correct 17% (01:08) wrong based on 248 sessions

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Tough and Tricky questions: Probability.

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.

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Re: 8 cities, including Memphis, are finalists to be chosen to host a poli  [#permalink]

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03 Nov 2014, 12:37
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Bunuel wrote:

Tough and Tricky questions: Probability.

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.

A = Memphis is chosen to host the convention
B = Memphis is not chosen to host the convention

We need to know either $$P(A)$$ or $$P(B)$$ since $$P(A) = 1-P(B)$$

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

$$P(B) = \frac{7}{8}$$ - SUFFICIENT

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

$$P(A) = \frac{1}{8}$$ - SUFFICIENT

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##### General Discussion
Manager
Joined: 10 Sep 2014
Posts: 97
8 cities, including Memphis, are finalists to be chosen to host a poli  [#permalink]

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14 Nov 2014, 10:43
statement 1: sufficient
we are being given exactly what the question is asking for

statement 2: sufficient
1- 1/8 = probability memphis is not chosen
Manager
Joined: 31 May 2015
Posts: 103
Re: 8 cities, including Memphis, are finalists to be chosen to host a poli  [#permalink]

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24 Jun 2016, 11:42
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1
Correct me if I am wrong but isn't the answer already on the argument

"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? "

There are 8 cities so 1-1/8= 7/8
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Re: 8 cities, including Memphis, are finalists to be chosen to host a poli  [#permalink]

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05 Sep 2018, 05:49
Top Contributor
1
Bunuel wrote:

Tough and Tricky questions: Probability.

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.

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

Cheers,
Brent
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Re: 8 cities, including Memphis, are finalists to be chosen to host a poli &nbs [#permalink] 05 Sep 2018, 05:49
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