Question:
Two cards are drawn at random from a standard pack of \(52\) cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...
Two cards are drawn at random from a standard pack of \(52\) cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...
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Count favourable pairs and divide by $\binom{52}{2}$.
Updated On: Oct 1, 2026
- \(\frac{7}{221}\)
- \(\frac{5}{221}\)
- \(\frac{8}{221}\)
- \(\frac{9}{221}\)
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The Correct Option is C
Solution and Explanation
Step 1: Count cases
There are \(12\) face cards (J, Q, K) and \(4\) aces. Face cards are taken as not including aces.
Favourable pairs: \(12\times4=48\).
Step 2: Total
\(\binom{52}{2}=1326\).
Step 3: Probability
\(\frac{48}{1326}=\frac{8}{221}\). Option (C).
Final Answer:
The probability is \(\frac{8}{221}\), option (C). \[ \boxed{\text{(C)}} \]
There are \(12\) face cards (J, Q, K) and \(4\) aces. Face cards are taken as not including aces.
Favourable pairs: \(12\times4=48\).
Step 2: Total
\(\binom{52}{2}=1326\).
Step 3: Probability
\(\frac{48}{1326}=\frac{8}{221}\). Option (C).
Final Answer:
The probability is \(\frac{8}{221}\), option (C). \[ \boxed{\text{(C)}} \]
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