The Reunion Committee is contemplating hiring a Photographer to take a group picture at the Sunday get together in Imperial Beach.
The committee is aware that, on average, people will blink their eyes about every six seconds and each blink will last about one tenth of a second.
The goal is a picture in which no one is blinking when the picture is taken.
But, the more people in the picture, the higher the probability someone will be blinking.
If we predict 100 people will be in the group picture, how many photographs must be taken to have a 95% probablity that no one is blinking?
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Answer
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The probability that an individual has his eyes open is 1 - 6(0.1)/60 = 0.99 and the probability that 100 people have
their eyes open is 0.99 exp(100) = 0.36603, or blinking = 0.63397 (Pc).
For N pictures, the probability that all pics have at least one person blinking is Pc exp(N) which must be less
than 0.05. N = ln(0.05)/ln(0.63397) = 6.57, so the photographer should take seven pictures.
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