1) What is the probability that two people have same birthday ?

2) What is the probability that two people have different birthday ?

Question

1)  What is the probability that
two people have same birthday ?
2)  What is the
probability that two people have different birthday ?

Lalit Mehra · Accepted Answer

Let A denote the event that two people have the same birthday.

$∴ \bar{A}$ denote the event that two people have different birthday.

Total number of days in year = 365

If two people have the same birthday, then their birthday could be on any one of the day from 365 days of the year.

∴ Number of cases in favour of event A = 1

Required probability, $P (A) = \frac{Favourable number of cases}{Total number of cases} = \frac{1}{365}$

We know that, P (A) + P $(\bar{A})$ = 1

$∴ \frac{1}{365} + P (\bar{A}) = 1 \Rightarrow P (\bar{A}) = 1 - \frac{1}{365} = \frac{364}{365}$

Probability that two people have the same birthday = $\frac{1}{365}$

Probability that two people have the same birthday = $\frac{364}{365}$