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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?

 Aug 3, 2017
 #1
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+1

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.

 Aug 3, 2017
 #2
avatar+98197 
+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%

 

 

cool cool cool

 Aug 3, 2017
edited by CPhill  Aug 3, 2017

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