A contest will consist of n questions, each of which is to be answered wither "True" or "False".
A contest will consist of n questions, each of which is to be answered wither "True" or "False". Anyone who answers all n questions 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 question will be a winner?
Answer/Solution
10
Steps/Work
(1/2)^n < 1/1000
(1/2)^n < (1/2)^3*(1/5)^3
Because 1/5 ~ (1/2)^2
n > 3 + 3*2 = 9
ANSWER: B
(1/2)^n < (1/2)^3*(1/5)^3
Because 1/5 ~ (1/2)^2
n > 3 + 3*2 = 9
ANSWER: B