Question

Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. The probability that first two cards are kings and the third card drawn is an ace is _____

• A. \( \frac{1}{135200} \)
• B. \( \frac{2}{5525} \)
• C. \( \frac{3}{5525} \)
• D. \( \frac{3}{135200} \)

Hint:

For without replacement, denominator keeps decreasing.

Answer 1

The Correct Option is B

Concept: Use multiplication rule for dependent events.
Step 1: First card is king. \[ \frac{4}{52} \]
Step 2: Second card is king. \[ \frac{3}{51} \]
Step 3: Third card is ace. \[ \frac{4}{50} \]
Step 4: \[ \text{Probability} = \frac{4}{52} \cdot \frac{3}{51} \cdot \frac{4}{50} = \frac{2}{5525} \]