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Question
From a pack of 52 cards, two are drawn one by one without replacement. Find the probability that both of them are kings.
Solution
Consider the given events.
A = A king in the first draw
B = A king in the second draw
\[\text{ Now } , \]
\[P\left( A \right) = \frac{4}{52} = \frac{1}{13}\]
\[P\left( B/A \right) = \text{ Getting a king in the second draw after getting a king in the first draw } \]
\[ = \frac{3}{51} \left[ \text{ After the first draw, the total number of cards will be 51 . Then, 3 kings will be remaining } . \right]\]
\[ = \frac{1}{17}\]
\[ \therefore \text
{ Required probability } = P\left( A \cap B \right) = P\left( A \right) \times P\left( B/A \right) = \frac{1}{13} \times \frac{1}{17} = \frac{1}{221}\]
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