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Question
A die is rolled. If the outcome is an odd number, what is the probability that it is prime?
Solution
Consider the given events.
A = The number is odd
B = The number is prime
Clearly,
A = {1, 3, 5}
B = {2, 3,5}
\[ \text{ Now } , \]
\[A \cap B = \left\{ 3, 5 \right\}\]
\[ \therefore \text{ Required probability } = P\left( B/A \right) = \frac{n\left( A \cap B \right)}{n\left( A \right)} = \frac{2}{3}\]
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