What is the Probability of Getting 16 Yes Answers in a Small Population Survey?

AI Thread Summary
The discussion revolves around calculating the probability of 16 out of 20 surveyed individuals answering 'yes' in a 35-person population. It highlights the assumption that those not surveyed have an equal chance of answering 'yes' or 'no'. A specific probability of 0.003% was mentioned for the scenario where all unsurveyed individuals answer 'no', prompting questions about the methodology behind this figure. Participants seek clarification on the probability of any individual responding 'yes' and the remaining population's impact on the overall probability. The conversation emphasizes the complexities of statistical probability in small population surveys.
moonman239
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Let's say I survey 20 people out of a 35-person population. 16 people answered yes to a particular question. What is the probability that only 16 people out of the total population would answer yes?

Attempt at a solution: The number of those not surveyed have an equal
probability of answering yes or no. Thus the probability of
those not surveyed all answering no is .003%.
 
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How did you get 0.003%?

What is the probability that any given individual will answer 'yes'?
How many people are remaining?
 

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