0
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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}

$\endgroup$
3
  • $\begingroup$ Why do I have to sum up the days? $\endgroup$
    – user233991
    Jan 24 '19 at 3:51
  • $\begingroup$ It could be Monday, it could be Tuesday, and so on. $\endgroup$ Jan 24 '19 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 '19 at 9:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.