A contest will consist of n questions, each of which is to be answered either "True" or "False". Anyone who answers all n questions correctly will be a winner. What i 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?
A> 5
B> 10
C> 50
D> 100
E> 1000
OA is B
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Contest - probability
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The probability that each of the questions are answered correctly is: 1/2
We are asked to find out the minimum number of questions that the contestant has to answer all correct so that the probability is less than 1/1000.
We have no option but to rely on the answer choices to get the answer. From my quick calculations I know that 2^5 is 32 & 2^10 is 1024. So, (1/2)^10 should be the answer because 1/1024 is smaller than 1/1000.
We are asked to find out the minimum number of questions that the contestant has to answer all correct so that the probability is less than 1/1000.
We have no option but to rely on the answer choices to get the answer. From my quick calculations I know that 2^5 is 32 & 2^10 is 1024. So, (1/2)^10 should be the answer because 1/1024 is smaller than 1/1000.
To get all questions correct Prob. will be multiplied.
Prob of getting 1st question True = 1/2
Prob of getting 1st & 2nd Question True = 1/2 * 1/2
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Prob of getting 1st & 2nd ...to 9th Question True = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/512
Prob of getting 1st & 2nd ...to 10th Question True = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/1024
Prob of getting 1st question True = 1/2
Prob of getting 1st & 2nd Question True = 1/2 * 1/2
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Prob of getting 1st & 2nd ...to 9th Question True = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/512
Prob of getting 1st & 2nd ...to 10th Question True = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/1024
