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Question
A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. Find the probability that the first card is a heart and the second card is a diamond if the first card is not replaced.
Solution
Consider the given events.
A = A heart in the first draw
B = A diamond in the second draw
\[\text{ Now } , \]
\[P\left( A \right) = \frac{13}{52} = \frac{1}{4}\]
\[P\left( B/A \right) = \frac{13}{51}\]
\[ \therefore \text{ Required probability }= P\left( A \cap B \right) = P\left( A \right) \times P\left( B/A \right) = \frac{1}{4} \times \frac{13}{51} = \frac{13}{204}\]
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