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Manhattan Question Set # 17

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Manhattan Question Set # 17

by richachampion » Wed Oct 12, 2016 7:42 am
Is the probability that Patty will answer all of the questions on her chemistry exam correctly greater than 50%?

(1) For each question on the chemistry exam, Patty has a 90% chance of answering the question correctly.
(2) There are fewer than 10 questions on Patty's chemistry exam.

OA: E
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Source: — Data Sufficiency |

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by [email protected] » Wed Oct 12, 2016 10:23 am
Hi richachampion,

We're asked if the probability that Patty will answer ALL of the question on her Exam is greater than 50%. This is a YES/NO question.

1) For each question on the chemistry exam, Patty has a 90% chance of answering the question correctly.

This Fact doesn't tell us the number of questions on the Exam - and THAT information is relevant.

IF... there's just 1 question, then there's a 90% chance of answer ALL of the questions correctly and the answer to the question is YES
IF... there are 2 questions, then there's a (.9)(.9) = 81% chance of answer ALL of the questions correctly (YES).
IF... there are 3 questions, then there's a (.9)(.9)(.9) = 72.9% chance of answer ALL of the questions correctly (YES).

However, as the number of questions increases, the percentage chance of answering ALL of the questions correctly decreases. At some point, the probability will fall below 50% and the answer to the question will become NO.
Fact 1 is INSUFFICIENT.

(2) There are fewer than 10 questions on Patty's chemistry exam.

This Fact tells us nothing about her chances of answering these questions correctly.
Fact 2 is INSUFFICIENT.

Combined, we know...
There are fewer than 10 questions
There's a 90% chance of answering each question correctly

From the work that we did in Fact 1, we know that with each additional question, the probability of answering ALL question correctly drops significantly. While you don't have to perform the actual calculation, it would not be hard to imagine that a 9 question Exam would have a considerably smaller probability (far less than 50%) than a 1, 2 or 3-question Exam. Thus, the answer could be YES or NO.
Combined, INSUFFICIENT

Final Answer: E

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