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Question
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and third card drawn is an ace?
Solution
Consider the given events.
A = A king in the first draw
B = A king in the second draw
C = An ace in the third draw
\[\text{ Now } , \]
\[P\left( A \right) = \frac{4}{52} = \frac{1}{13}\]
\[P\left( B/A \right) = \frac{3}{51} = \frac{1}{17}\]
\[P\left( C/A \cap B \right) = \frac{4}{50} = \frac{2}{25}\]
\[ \therefore \text{ Required probability } = P\left( A \cap B \cap C \right)\]
\[ = P\left( A \right) \times P\left( B/A \right) \times P\left( C/A \cap B \right)\]
\[ = \frac{1}{13} \times \frac{1}{17} \times \frac{2}{25}\]
\[ = \frac{2}{5525}\]
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