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Question
Two cards are drawn without replacement from a pack of 52 cards. Find the probability that the first is a king and the second is an ace.
Solution
Consider the given events
A = A king in the first draw
B = An ace in the second draw
\[\text{ Now } , \]
\[P\left( A \right) = \frac{4}{52} = \frac{1}{13}\]
\[P\left( B/A \right) = \frac{4}{51} = \frac{4}{51}\]
\[ \therefore \text{ Required probability } = P\left( A \cap B \right)\]
\[ = P\left( A \right) \times P\left( B/A \right)\]
\[ = \frac{1}{13} \times \frac{14}{51}\]
\[ = \frac{4}{663}\]
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