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sasho [114]
1 year ago
8

The probability of meeting a random person who has the same birthday as you is365• whichis approximately 0.27%. What is the prob

ability that the 25th person you meet is the firstperson who has the same birthday as you?00.27%00.14%00.25%00.03%
Mathematics
1 answer:
Zepler [3.9K]1 year ago
6 0

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}

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