Question

In a simultaneous throw of a  pair of dice, find the probability of getting:

a sum greater than 9

Answer 1

\[\text{ When a pair of dice is thrown simultaneously, the sample space will be as follow }: \]
\[S = \left\{ \left( 1, 1 \right), \left( 1, 2 \right), \left( 1, 3 \right), \left( 1, 4 \right), \cdots\left( 6, 5 \right), \left( 6, 6 \right) \right\}\]
\[\text{ Hence, the total number of outcomes is 36 } . \]

\[\text{ Let A be the event of getting pairs whose sum is greater than 9 } . \]
\[\text{ The pairs whose sum is greater than 9 are } \left( 4, 6 \right), \left( 5, 5 \right), \left( 5, 6 \right), \left( 6, 4 \right), \left( 6, 5 \right) \text{ and } \left( 6, 6 \right) . \]
\[\text{ Hence, the number of favorable outcomes is 6 } . \]
\[ \therefore P\left( A \right) = \frac{\text{ Number of favourable outcomes }}{\text{  Total number of outcomes }} = \frac{6}{36} = \frac{1}{6}\]