# Birthday Problem [closed]

What is the approximate probability (in percentage) that at least $2$ people in a group of $6$ randomly-selected have a birthday on the same day of the week?

## closed as off-topic by Jean-Claude Arbaut, AlexR, Najib Idrissi, Surb, N. F. TaussigApr 15 '15 at 9:49

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Jean-Claude Arbaut, AlexR, Najib Idrissi, Surb, N. F. Taussig
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• en.wikipedia.org/wiki/Birthday_problem – Surb Apr 15 '15 at 8:51
• The general problem even has the same name. Plugging it into google will give you a lot of helpful references wich you can use to at least do something of your own and show your work. – AlexR Apr 15 '15 at 9:02

$1-\frac{365*(365-7)*(365-14)*(362-21)*(361-28)*(360-35)}{365^6}$
• Why do you subtract multiples of $7$? – Jean-Claude Arbaut Apr 15 '15 at 9:23
• Because in the second term I am calculating the probability of no two people sharing the same birthday week. Hence $-7$. – Aditya Agarwal Apr 15 '15 at 9:43
• There are roughly $52$ weeks in a year: $52$ mondays, $52$ tuesdays... Here no two people must share the same day of week. – Jean-Claude Arbaut Apr 15 '15 at 9:46