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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 heart and second is red.
Solution
Consider the given events.
A = A heart in the first throw
B = A red card in the second throw
\[\text{ Now } , \]
\[P\left( A \right) = \frac{13}{52} = \frac{1}{4}\]
\[P\left( B/A \right) = \frac{25}{51}\]
\[ \therefore \text{ Required probability } = P\left( A \cap B \right)\]
\[ = P\left( A \right) \times P\left( B/A \right)\]
\[ = \frac{1}{4} \times \frac{25}{51}\]
\[ = \frac{25}{204}\]
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