Question: 2019 Fall Midterm - 16
Consider 4 people, each of which has a uniformly random birthday. We ignore leap years; thus, one year
has 365 days. Define the event
- A = "at least 2 of these 4 people have the same birthday".
(a)
${4 \choose 2} \cdot \frac{1}{365}$
(b)
${4 \choose 2} \cdot \frac{1}{365} + {4 \choose 3} \cdot \frac{1}{365^2} + {4 \choose 4} \cdot \frac{1}{365^3}$
(c)
$1 - \frac{362 \cdot 363 \cdot 364}{365^3}$
(d)
$1 - \frac{361 \cdot 362 \cdot 363 \cdot 364}{365^4}$