Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.

Given:

Two unbiased dice are thrown.

To do:

We have to find the probability that the total of the numbers on the dice is greater than 10.

Solution:

Two unbiased dice are thrown.

This implies,

The total number of possible outcomes $n=6\times6=36$.

Outcomes, where the total of the numbers on the dice is greater than 10 (i.e., 11 and 12), are $(5, 6), (6, 5), (6, 6)$

Total number of favourable outcomes $=3$.

We know that,

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability that the total of the numbers on the dice is greater than 10 $=\frac{3}{36}$

$=\frac{1}{12}$

The probability that the total of the numbers on the dice is greater than 10 is $\frac{1}{12}$.