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Question
An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?
Solution
Consider the given events.
A = A black ball in the first draw
B = A black ball in the second draw
\[\text{ Now } , \]
\[P\left( A \right) = \frac{10}{15} = \frac{2}{3}\]
\[P\left( B/A \right) = \frac{9}{14}\]
\[ \therefore \text{ Required probability } = P\left( A \cap B \right) = P\left( A \right) \times P\left( B/A \right) = \frac{2}{3} \times \frac{9}{14} = \frac{3}{7}\]
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