Question

From a well shuffled pack of \(52\) cards, two cards are drawn at random. Then, the probability of both the cards being kings is:

• A. \(\dfrac{1}{15}\)
• B. \(\dfrac{25}{57}\)
• C. \(\dfrac{35}{256}\)
• D. \(\dfrac{1}{221}\)

Hint:

When cards are drawn without replacement, use either combinations \[ P=\frac{{}^{m}C_{r}}{{}^{n}C_{r}} \] or multiply successive probabilities. Both methods give the same result.

Answer 1

The Correct Option is D

Step 1: Count favorable and total outcomes.
Total ways to draw 2 cards from 52: \(\binom{52}{2}=1326\). Ways to draw 2 kings from 4: \(\binom{4}{2}=6\).

Step 2: Compute probability.
\[P = \frac{6}{1326} = \frac{1}{221}.\]
\[\boxed{\frac{1}{221}}\]