Question 1187672
.
What is the probability that at least 2 people in a group of 8 people have the same birthdate? 
(Assume every year has exactly 365 days  -  i.e., there is no Leap Day.)
~~~~~~~~~~~~~



<pre>
This probability is the COMPLEMENT to the probability that ALL 8 people have DIFFERENT birthdays.


The probability that 8 people have different birthdays is


    Q = {{{(364/365)*(363/365)*(362/365)*(361/365)*(360/365)*(359/365)*(358/365)}}} = 


             //  (the product of 7 (seven)  multipliers) = 0.925665...


Thus the probability under the problem's question is


    P = 1 - Q = 1 - {{{(364/365)*(363/365)*(362/365)*(361/365)*(360/365)*(359/365)*(358/365)}}} = 1 - 0.925665... = 0.0743  (rounded).    <U>ANSWER</U>
</pre>

Solved.


----------------


See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Coinciding-birthdays.lesson>Coinciding birthdays</A> 

in this site.