What is the probability of two people being born on the same day of the week?

I understand both of them individually have probability of 1/7 to be born on a certain day and that the two probabilities are independent of one another. So the answer could be 1/49. But that's a wrong answer.


1 Answer 1


You still have to sum up the days.

Let $A$ be the day that the first person is born on and $B$ be the day for the second person.

\begin{align} Pr(A=B) = \sum_{i=1}^7 Pr(A=i)Pr(B=i)=\frac17 \end{align}

  • $\begingroup$ Why do I have to sum up the days? $\endgroup$
    – user233991
    Jan 24, 2019 at 3:51
  • $\begingroup$ It could be Monday, it could be Tuesday, and so on. $\endgroup$ Jan 24, 2019 at 3:51
  • 1
    $\begingroup$ @user233991: A similar problem (but using 6 instead of 7) is the probability two fair dice will show the same number. That problem is found in many elementary probability books, and the answer is 1/6. $\endgroup$
    – BruceET
    Jan 24, 2019 at 9:37

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