The probability of randomly drawing five cards from a deck that has exactly one Ace is ______.
Step-by-Step Solution
Key Concept: Use hypergeometric distribution: multiply combinations for favorable outcomes (1 Ace and 4 non-Aces) divided by total combinations.
We need to find the probability of drawing exactly one Ace when drawing 5 cards from a standard 52-card deck. There are 4 Aces total. The number of ways to choose exactly 1 Ace from 4 is $\binom{4}{1}$, and the number of ways to choose 4 non-Ace cards from the remaining 48 cards is $\binom{48}{4}$. The total ways to draw 5 cards is $\binom{52}{5}$. Therefore, $P = \frac{\binom{4}{1} \cdot \binom{48}{4}}{\binom{52}{5}} = \frac{4 \cdot 194580}{2598960} \approx 0.299$.
Correct Answer: 0.299