This is from "99 more 700+ GMAT questions" that some good soul posted on this web site.
N questions can either be true or false. If you answer all N correct, you win. What is the least value of N for which the probability is less than 1/1000 for you to win by guessing randomly?
a. 5
b. 10
c. 50
d. 100
e. 1000
(apparently, the correct answer is B)
Now, my logic is this: this is sort of like tossing a coin. You always have a 50% chance to win. Winning (i.e., guessing right) on N questions would then be 1/2 times 1/2 times 1/2... or (1/2)^N (1/2 to the power of N).
2^14 is 512; 2^15 is 1024. So, your probability to win if you have 14 questions is 1/512>1/1000. Probability to win if you have 15 questions is 1/1024<1/1000. So the correct answer to this question would have to be N>14; of the answer choices above, it would be C, 50.
Thoughts/ideas? Any tips are much appreciated! I'm less than a week away from GMAT, and probability/permutations is definitely my weak link. Thanks, guys!
N questions can either be true or false. If you answer all N correct, you win. What is the least value of N for which the probability is less than 1/1000 for you to win by guessing randomly?
a. 5
b. 10
c. 50
d. 100
e. 1000
(apparently, the correct answer is B)
Now, my logic is this: this is sort of like tossing a coin. You always have a 50% chance to win. Winning (i.e., guessing right) on N questions would then be 1/2 times 1/2 times 1/2... or (1/2)^N (1/2 to the power of N).
2^14 is 512; 2^15 is 1024. So, your probability to win if you have 14 questions is 1/512>1/1000. Probability to win if you have 15 questions is 1/1024<1/1000. So the correct answer to this question would have to be N>14; of the answer choices above, it would be C, 50.
Thoughts/ideas? Any tips are much appreciated! I'm less than a week away from GMAT, and probability/permutations is definitely my weak link. Thanks, guys!
