Question

Two cards are drawn successively without replacement from a well-shuffled deck of 52 cards. Find the probability of exactly one ace.

Answer 1

\[P\left( \text{ exactly one ace } \right) = P\left( \text{ first card is ace }  \right) + P\left( \text{ second card is ace } \right)\]
\[ = \frac{4}{52} \times \frac{48}{51} + \frac{48}{52} \times \frac{4}{51}\]
\[ = \frac{192 + 192}{52 \times 51}\]
\[ = \frac{384}{52 \times 51}\]
\[ = \frac{32}{221}\]