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} =(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:

`=(1)/(365)`

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

`\begin{gathered} =1-(1)/(365) \\ \\ =(365-1)/(365) \\ \\ =(364)/(365) \end{gathered}`

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

Therefor,

`\begin{gathered} P=((364)/(365))^(24)*(1)/(365) \\ \\ =(0.9972)^(24)*0.27 \\ \\ =0.9362*0.27 \\ \\ =0.25\% \end{gathered}`