In a simultaneous throw of a pair of dice, find the probability of getting 5 at least once.

Given:

Two dice are thrown simultaneously. 

To do:

We have to find the probability of getting 5 at least once.

Solution:

When two dice are thrown, the total possible outcomes are $6\times6=36$.

This implies,

The total number of possible outcomes $n=36$

Outcomes where we get 5 at least once are $[(1, 5), (2, 5), (3, 5), (4, 5), (6, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)]$

Total number of favourable outcomes $=11$

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

Therefore,

Probability of getting 5 at least once $=\frac{11}{36}$

The probability of getting 5 at least once is $\frac{11}{36}$.