Question

Let x be a random variable giving the number of aces in a random draw of 4 cards from an ordinary deck of 52 cards. construct a table showing the probability distribution of x

Answer 1

$\mathbb P(X=x)=\begin{cases}\dfrac{\binom{48}4\binom40}{\binom{52}4}\approx0.7187&\text{for }x=0\\\\\dfrac{\binom{48}3\binom41}{\binom{52}4}\approx0.2556&\text{for }x=1\\\\\dfrac{\binom{48}2\binom42}{\binom{52}4}\approx0.0250&\text{for }x=2\\\\\dfrac{\binom{48}1\binom43}{\binom{52}4}\approx0.0007&\text{for }x=3\\\\\dfrac{\binom{48}0\binom44}{\binom{52}4}\approx0.0000037&\text{for }x=4\\\\0&\text{otherwise}\end{cases}$