Question: 2015 Fall Final - 14
Let $n$ be the number of students who are writing this exam. Each of these students has a uniformly
random birthday, which is independent of the birthdays of the other students. We ignore leap years;
thus, the year has 365 days. Define the event
- A = "at least one student's birthday is on December 21".
(a)
$1 - (1/365)^{n}$
(b)
$1 - (364/365)^{n}$
(c)
$n \cdot (1/365) \cdot (364/365)^{n-1}$
(d)
$365 \cdot n \cdot (364/365)^{n-1}$