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Question: 2018 Fall Midterm - 16

Author: Michiel Smid
Alexa, Tri, and Zoltan each have a uniformly random birthday. (We ignore leap years, so that one year has 365 days.)
Define the event
  • A = "Alexa, Tri, and Zoltan have different birthdays".
What is $\text{Pr}(A)$?
(a)
$\frac{362 \cdot 363 \cdot 364}{365^3}$
(b)
$\frac{365^2}{363 \cdot 364}$
(c)
$\frac{363^3}{362 \cdot 363 \cdot 364}$
(d)
$\frac{363 \cdot 364}{365^2}$