GMAT prep

Probability of answering true = prob of answering false = 1/2

We are asked to find n where

(1/2)^n < 1/1000

We know (1/2)^10 = 1/1024 < 1/1000

Hence n = 10

Consider a simple example; Say there are 4 questions; and each question can have 2 possible answers (i.e. either True or False), total possible outcomes would be 2*2*2*2 (or 2^4); If all the questions were to be answered correctly total outcomes would be 1*1*1*1 (First question – Right, Second question – Right, Third Question – Right and 4th Question Right) or 1 outcome; Hence probability would be 1^4 or 1

Now here the total questions are “n”; so total possible outcomes are 2^n; when all questions are answered correctly total possible outcomes would be 1^n or 1; Hence probability = 1^n / 2^n

Keeping the condition in mind 1^n / 2^n < 1/1000
Or 1 / 2^n < 1 / 1000
Multiplying each side by 1000
1000 < 2^n
2^10 = 1024 and 2^9 = 512; so least value of n to satisfy the limitation would be n=10

Correct Answer is B 10.
And i guess the explanations are good. I agree with them