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

Step 1: Understanding the Concept:
Since cards are drawn without replacement, the total number of cards and the number of specific cards decrease with each draw. This is a case of dependent events.
Step 2: Formula Application:
1. Probability of 1st King ($K_1$) = $4/52$
2. Probability of 2nd King ($K_2$) = $3/51$ (one King and one card removed)
3. Probability of 3rd Ace ($A_3$) = $4/50$ (two cards removed, but all 4 Aces remain)
Step 3: Explanation:
Total Probability = $\frac{4}{52} \times \frac{3}{51} \times \frac{4}{50}$ $$P = \frac{1}{13} \times \frac{1}{17} \times \frac{2}{25} = \frac{2}{13 \times 17 \times 25} = \frac{2}{5525}$$
Step 4: Final Answer:
The probability is $2/5525$.