SOLUTION: Determine the probability that in a class of 8 students, at least two students have the same birthday. Assume that there are always 365 days in a year and that birth rates are cons

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Question 510573: Determine the probability that in a class of 8 students, at least two students have the same birthday. Assume that there are always 365 days in a year and that birth rates are constant throughout the year. (Hint: First determine the probability that no two students have the same birthday and then apply the complementation rule.)


Please help! Thanks, Sue
Answer by stanbon(75887) About Me  (Show Source):
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Determine the probability that in a class of 8 students, at least two students have the same birthday. Assume that there are always 365 days in a year and that birth rates are constant throughout the year. (Hint: First determine the probability that no two students have the same birthday and then apply the complementation rule.)
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1st: 1
2nd: (1-(1/365)) = (364/365
3rd: (1-(2/365)) = (363/365
4th: (1-(3/365)) = (362/365
...
8th: (1-(7/365)) = (358/365)
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P(no 2 of 8 have the same birthday) = [1(364)(363)(362)...(358)]/365^7
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= 0.9257
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P(2 have the same birthday) = 1 - 0.9257 = 0.0743
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Cheers,
Stan H.