document.write( "Question 1118481: What is the probability that there are at least two people with the same birthday in a class of 40? \n" ); document.write( "

Algebra.Com's Answer #733828 by math_helper(2461) $\"\"$ $\"About$

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P(at least two people share a birthday) = 1 - P(no two people share a birthday)
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\n" ); document.write( "\n" ); document.write( "The 1st person has some birthday...
\n" ); document.write( "The 2nd person has 364 possible non-matching birthdaysЕ
\n" ); document.write( " That leaves 363 non-matching birthdays for the 3rd person
\n" ); document.write( " etc.

\n" ); document.write( "Extending this to 40 people:
\n" ); document.write( "P(no two people share a birthday) = $\"+%28364%2F365%29%28363%2F365%29+\"$ * Е * $\"+%28327%2F365%29%28326%2F365%29+\"$ = 0.1088
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\n" ); document.write( "\n" ); document.write( "P(two or more people share a birthday) = 1 - 0.1088 = $\"+highlight%28matrix%281%2C3%2C+%22+%22%2C+%220.8912%22%2C+%22+%22%29+%29+\"$
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\n" ); document.write( "\n" ); document.write( "So in a class of 40, it is far more likely that two or more people share the same birthday than for no two people to share a birthday. [ It only takes 23 people to reach a probability of >50% that two people will share the same birthday ]. If this seem nonintuitive, note that the above gives the probability that ANY two people share a birthday. If you are in a class of 40 students, the probability that someone also has YOUR birthday is still a pretty small number (about 1/10).
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\n" ); document.write( "Edit 6/11: Tutor @Shin123 has arrived at an incorrect answer, using an incorrect method. \n" ); document.write( "

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