Respuesta :
Given:
The same birthday probability is
[tex]\begin{gathered} =\frac{1}{365} \\ \\ =0.27\% \end{gathered}[/tex]Find:-
Person who has the same birthday
Explanation-:
The probability of meeting a random person who has the same birthday is:
[tex]=\frac{1}{365}[/tex]Probability of meeting a random person who does not has same birthday as you
[tex]\begin{gathered} =1-\frac{1}{365} \\ \\ =\frac{365-1}{365} \\ \\ =\frac{364}{365} \end{gathered}[/tex]The required probability that the 25th person you meet is the first person who has the same birthday as
[tex]\begin{gathered} =\text{ Probability that the first 24 persons we meet did not have same birthday \rparen}\times(\text{ probability that the first 25 person we meet has same birthday\rparen} \\ \end{gathered}[/tex]Therefor,
[tex]\begin{gathered} P=(\frac{364}{365})^{24}\times\frac{1}{365} \\ \\ =(0.9972)^{24}\times0.27 \\ \\ =0.9362\times0.27 \\ \\ =0.25\% \end{gathered}[/tex]