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.