Question: 2016 Fall Final - 16
Let $n \geq 2$ 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 two students have their birthday on December 14".
(a)
${\sum_{k=2}^{n}} {n \choose k} \cdot \left( \frac{1}{365} \right)^k$
(b)
$1 - \left( \frac{364}{365} \right)^n - n \cdot \frac{1}{365} \cdot \left( \frac{364}{365} \right)^{n-1}$
(c)
${n \choose 2} \cdot \left( \frac{1}{365} \right)^2 \cdot \left( \frac{364}{365} \right)^{n-2}$
(d)
$1 - {n \choose 2} \cdot \left( \frac{1}{365} \right)^2 \cdot \left( \frac{364}{365} \right)^{n-2}$