People Equals

Probability Level 2

In a survey of the street, each respondent answered eight questions, your answer may be yes or no to each question. What is the minimum number of respondents to make sure that two persons also answered Equal all the questions ?


The answer is 257.

Gabriel Merces by Gabriel Merces , 23, Brazil

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2 solutions

Vaishnavi Gupta
Mar 21, 2014

The total number of possible ways of answering 8 questions is with either Yes or NO is : 2^8. Therefore, if there are 2^8 + 1 respondents, then definitely, at least two of them will give the same set of answers.

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Vaibhav Jain
Mar 1, 2014

You just have to think that 2 persons will surely respond equally when all other possibilities of answering were not left. So, Total ways of answering is 2^8=256. It means minimum number of people required was 257.

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