Practice By Tag: The Birthday Paradox

Question: 2014 Winter Final - 13

1 . Let $A = \{1,2,3,\dots,100\}$. Let $x$, $y$, and $z$ be elements in $A$ that are chosen independently and uniformly at random. What is the probability that $x = y = z$?

(a)

$\frac{1}{{100 \choose 2}}$

(b)

$\frac{1}{100}$

(c)

$\frac{1}{100 \cdot 99}$

(d)

$\frac{1}{100 \cdot 100}$