document.write( "Question 385347: What is the probability that 2 (or more) people in a random group of 25 people have a common birthday? (This is the famous Birthday Paradox Problem.) \n" ); document.write( "

Algebra.Com's Answer #272699 by sudhanshu_kmr(1152) $\"\"$ $\"About$

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\n" ); document.write( "Here we firstly find the probability of event when all 25 people have different birthday...\r
\n" ); document.write( "\n" ); document.write( " probability of first people have its own birthday = 365/365 ( sure )\r
\n" ); document.write( "\n" ); document.write( " probability of second people have different b'day to first = 364/365
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\n" ); document.write( " probability of third people have different b'day to first and second = 363/365
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\n" ); document.write( "similarly for 25th person, probability of different b'day = 341/365\r
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\n" ); document.write( "\n" ); document.write( "probability when all have different b'day P(A) = 365/365 * 364/365 *.....*341/365\r
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\n" ); document.write( "\n" ); document.write( " = (1/365)^24 * ( 364 *.....*341) \r
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\n" ); document.write( "\n" ); document.write( "now, probability that 2 or more people have common b'day = P(A')\r
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\n" ); document.write( "\n" ); document.write( "= 1-P(A)\r
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