Question

The probability of meeting a random person who has the same birthday as you is365• whichis approximately 0.27%. What is the probability that the 25th person you meet is the firstperson who has the same birthday as you?00.27%00.14%00.25%00.03%

Answer 1

Given:

The same birthday probability is

$\begin{gathered} =\frac{1}{365} \\ \\ =0.27\% \end{gathered}$

Find:-

Person who has the same birthday

Explanation-:

The probability of meeting a random person who has the same birthday is:

$=\frac{1}{365}$

Probability of meeting a random person who does not has same birthday as you

$\begin{gathered} =1-\frac{1}{365} \\ \\ =\frac{365-1}{365} \\ \\ =\frac{364}{365} \end{gathered}$

The required probability that the 25th person you meet is the first person who has the same birthday as

$\begin{gathered} =\text{ Probability that the first 24 persons we meet did not have same birthday \rparen}\times(\text{ probability that the first 25 person we meet has same birthday\rparen} \\ \end{gathered}$

Therefor,

$\begin{gathered} P=(\frac{364}{365})^{24}\times\frac{1}{365} \\ \\ =(0.9972)^{24}\times0.27 \\ \\ =0.9362\times0.27 \\ \\ =0.25\% \end{gathered}$