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# probability

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Assume 365 days per year. If 15 people are selected at random, what is the probability that at least two of them will have the same birthday?

Guest Aug 3, 2017
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#1
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The probability is =1 - [365P15 / 365^15] =

1 - [2.031285348831 x 10^38 / 2.7188983230290 x 10^38]

1 - 0.74709868 = 0.25290131 x 100 =25.29% - The probability that any two will share the same birthday.

Guest Aug 3, 2017
#2
+76833
+1

The probability that at least two share a birthday is   1 - P( that none share a birthday )

And the probability that none share a birthday is given by :

[ 365 * 364 * 363 * .....* 352 * 351 ] /  [ 350 ! *  365^15]  =

[ 365 ! ] /  [350 ! * 365^15]  ≈ .747

So... 1 - .747  ≈ .253  ≈  25.3%

CPhill  Aug 3, 2017
edited by CPhill  Aug 3, 2017

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