A contest will consist of n questions and each question to be answered either ‘true’ or ‘false’. Anyone who answers all questions correctly will be the 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 question will be the winner?
Please explain. OA to follow shortly.
Probability of answering a Question right = 1/2
N Questions is 1/2 X 1/2 X 1/2 ... n times means (1/2) ^ n
We need to find least n such that (1/2) ^ n < 1/1000
If n =5 1/32 > 1/1000
n =10 1/1024 < 1/1000