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प्रश्न
Two dice are thrown and it is known that the first die shows a 6. Find the probability that the sum of the numbers showing on two dice is 7.
उत्तर
Consider the given events.
A = First die shows 6
B = The sum of the numbers on two dice is 7.
Clearly,
A= {(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
B = {(2, 5), (5, 2), (4, 3), (3, 4), (1, 6), (6, 1)}
\[\text{ Now } , \]
\[A \cap B = \left\{ \left( 6, 1 \right) \right\}\]
\[ \therefore \text{ Required probability } = P\left( B/A \right) = \frac{n\left( A \cap B \right)}{n\left( A \right)} = \frac{1}{6}\]
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