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mysseo: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Tue Nov 15, 2011 3:28 pm; Thanked: 1 times

contest winner

by mysseo » Mon Jan 02, 2012 10:43 pm

A contest will consist of N questions, each of which is to be answered either "True" or "False". Anyone who answers all N questions correctly will be a winner. What is the least value of N for which the probability is less than 1/1,000 that a person who randomly guessing the answer to each question will be a winner?

A. 5
B. 10
C. 50
D. 100
E. 1,000

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Source: Beat The GMAT — Problem Solving | Mon Jan 02, 2012 10:43 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Mon Jan 02, 2012 10:58 pm

mysseo wrote:A contest will consist of N questions, each of which is to be answered either "True" or "False". Anyone who answers all N questions correctly will be a winner. What is the least value of N for which the probability is less than 1/1,000 that a person who randomly guessing the answer to each question will be a winner?

A. 5
B. 10
C. 50
D. 100
E. 1,000

Probability of guessing the correct answer = 1/2
So, for N questions, the probability of guessing the correct answer = (1/2)^N
Now, (1/2)^N < 1/1000
If N = 5, then 1/32 < 1/1000 is not true.
If N = 10, then 1/1024 < 1/1000 is true.

The correct answer is B.

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mysseo: Senior | Next Rank: 100 Posts; Posts: 38; Joined: Tue Nov 15, 2011 3:28 pm; Thanked: 1 times

by mysseo » Mon Jan 02, 2012 11:05 pm

Thank you Anurag,
"The probability of guessing the correct answer is 1/2" is the key to the solution. I couldn't think of this when I first encountered this problem.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Mon Jan 02, 2012 11:06 pm

mysseo wrote:Thank you Anurag,
"The probability of guessing the correct answer is 1/2" is the key to the solution. I couldn't think of this when I first encountered this problem.

Welcome.

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ArunangsuSahu: Master | Next Rank: 500 Posts; Posts: 382; Joined: Thu Mar 31, 2011 5:47 pm; Thanked: 15 times

by ArunangsuSahu » Tue Jan 03, 2012 7:34 pm

This is a PROBABILITY Question:
1. Each question can have 2 possibilities. "TRUE" or "FALSE"

So for N questions total 2^N possibilities =Sample Space.

There is only one way all questions get corrected

so according to the question
1/2^N<1/1000

N=10

(B) is the answer