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Question
In a simultaneous throw of a pair of dice, find the probability of getting:
an even number on one and a multiple of 3 on the other
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Solution
\[\text{ When a pair of dice is thrown simultaneously, the sample space will be as follow }: \]
\[S = \left\{ \left( 1, 1 \right), \left( 1, 2 \right), \left( 1, 3 \right), \left( 1, 4 \right), \cdots\left( 6, 5 \right), \left( 6, 6 \right) \right\}\]
\[\text{ Hence, the total number of outcomes is 36 } . \]
\[\text{ Let A be the event of getting pairs with an even number on one die and a multiple of 3 on the other }. \]
\[\text{ The pairs with an even number on one die and a multiple of 3 on the other are } \left( 2, 3 \right), \left( 2, 6 \right), \left( 4, 3 \right), \left( 4, 6 \right), \left( 6, 3 \right) \text{ and } \left( 6, 6 \right) . \]
\[\text{ Hence, the number of favourable outcomes is 6 }. \]
\[ \therefore P\left( A \right) = \frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }} = \frac{6}{36} = \frac{1}{6}\]
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