Question

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

a sum less than 7

Answer 1

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

\[\text{ Let A be the event of getting pairs whose sum is less than 7 } . \]
\[\text{ The pairs whose sum is less than 7 are } \left( 1, 1 \right), \left( 1, 2 \right), \left( 1, 3 \right), \left( 1, 4 \right), \left( 1, 5 \right), \left( 2, 1 \right), \left( 2, 2 \right), \left( 2, 3 \right), \left( 2, 4 \right), \left( 3, 1 \right), \left( 3, 2 \right), \left( 3, 3 \right), \left( 4, 1 \right), \left( 4, 2 \right) \text{ and } \left( 5, 1 \right) . \]
\[\text{ Hence, the number of favourable outcomes is }15 . \]
\[ \therefore P\left( A \right) = \frac{\text{ Number of favourable outcomes }}{\text{ Total number of outcomes }} = \frac{15}{36} = \frac{5}{12}\]