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#### PP1: A contest consists of n questions, each answered

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 Post subject: PP1: A contest consists of n questions, each answered  Posted: Tue May 13, 2008 4:48 pm
 A contest consists of n questions, each answered either True or False. Anyone who answers all n correctly will be a winner. What is the least value of n for which the probability is Less than 1/ 1000 that a person who randomly guesses the answer to each will be a winner. Answer: 10. Had absolutely no clue where to begin with this one...no probability theory i could think to apply helped in any way! Simply stuck! Thanks

 Post subject: Re: PP1: A contest consists of n questions, each answered  Posted: Wed May 14, 2008 5:48 am
 ManhattanGMAT Staff

Posts: 8087
 Anonymous wrote:A contest consists of n questions, each answered either True or False. Anyone who answers all n correctly will be a winner. What is the least value of n for which the probability is Less than 1/ 1000 that a person who randomly guesses the answer to each will be a winner.Answer: 10.Had absolutely no clue where to begin with this one...no probability theory i could think to apply helped in any way!Simply stuck!Thanks rephrase: what is the least value of n for which there is less than a 1/1000 chance of guessing n questions in a row correctly?' here's the deal: * there is a 1/2 chance of guessing each question correctly * each question is independent of the other questions, so the chance of guessing n questions correctly is (1/2)(1/2)(1/2)...(1/2), where there are n (1/2)'s * this is (1/2)^n, or 1/(2^n) so: 1/2^n < 1/1000 take reciprocals: 2^n > 1000 n > 10 (because 2^10 = 1024) i've seen big powers of two in gmatprep problems before, but 2^10 is definitely the biggest i've yet seen.

 Post subject: Re: PP1: A contest consists of n questions, each answered  Posted: Fri Aug 17, 2012 11:26 pm
 Students

Posts: 1
 HiI had a small doubt on the above expln. No where in the question does he mention that true and false are equally likely. So we jus assume that they are equally probable and go ahead and take the probablity to be 1/2 ?Thanks

 Post subject: Re: PP1: A contest consists of n questions, each answered  Posted: Sun Aug 19, 2012 3:41 pm
 ManhattanGMAT Staff

Posts: 2390
 jyothi.11182 wrote:HiI had a small doubt on the above expln. No where in the question does he mention that true and false are equally likely. So we jus assume that they are equally probable and go ahead and take the probablity to be 1/2 ?ThanksThe question says that the contestant will "randomly" guess answers to the questions. When I randomly guess answers I have an equal chance of getting each answer. For example, if I took the GMAT but just picked the first letter I felt like picking for each question, I would have a 1/5 chance of answering correctly. Similarly a person "randomly" answering (or in other words, not trying at all, just picking a "random" answer) in this scenario would have a 1/2 chance of getting each question correct. _________________Jamie NelsonManhattanGMAT Instructor

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