Question 1184147
.
Five people gather for a dinner party. Compute the probability that no two of them
have the same birthday. (Hint: use 365 days for a year).
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<pre>
1-st person has his (or her) birthday at some day of the year.


The probability that the 2-nd person has his (or her) birthday at some other of remaining 364 days is  {{{364/365}}}.

The probability that the 3-rd person has his (or her) birthday at some other of remaining 363 days is  {{{363/365}}}.

The probability that the 4-th person has his (or her) birthday at some other of remaining 362 days is  {{{362/365}}}.

The probability that the 5-th person has his (or her) birthday at some other of remaining 361 days is  {{{361/365}}}.


The final probability is  {{{(364/365)*(363/365)*(362/365)*(361/365)}}} = 0.9729   (rounded).    <U>ANSWER</U>
</pre>

Solved.


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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.