Question

Two friends were born in 2000. What is the probability that they have the same birthday?
(a) $\frac{1}{365}$
(b) $\frac{1}{366}$
(c) $\frac{2}{365}$
(d) $\frac{1}{183}$

Answer 1

(b) $\frac{1}{366}$

Explanation:
The year 2000 was a leap year. So, it had 366 days.
One friend's birthday may fall on any one of the 366 days and the other friend's birthday may fall on any one of the 366 days.

Total number of ways in which the birthdays of the two friends fall on particular days = (366 x 366)
The favourable outcomes for both friends to have the same birthday out of the 366 days = 366
∴ P( both have the same birthday) = $\frac{366}{\left(366\times 366\right)}=\frac{1}{366}$