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प्रश्न
In a simultaneous throw of a pair of dice, find the probability of getting:
a doublet of prime number
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उत्तर
\[\text{ When a pair of dice is thrown simultaneously, the sample space will be as follow }: \]
\[S = \left\{ \left( 1, 1 \right), \left( 1, 2 \right), \left( 1, 3 \right), \left( 1, 4 \right), \cdots\left( 6, 5 \right), \left( 6, 6 \right) \right\}\]
\[\text{ Hence, the total number of outcomes is 36 } . \]
\[\text{ Let A be the event of getting doublets of prime numbers in the sample space } . \]
\[\text{ The doublets of prime numbers in the sample space are } \left( 2, 2 \right), \left( 3, 3 \right) \text{ and } \left( 5, 5 \right) . \]
\[\text{ Hence, the number of favourable outcomes is 3 } . \]
\[ \therefore P\left( A \right) = \frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }} = \frac{3}{36} = \frac{1}{12}\]
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