Question

Find the chance of throwing a $5$ or $6$ atleast once in four throws of a single die.

Answer 1

In one throw of dice, we have $\frac{2}{6}$ i.e., $\frac{1}{3}$ chance of throwly a dice for five or $6$.
So, we have $\frac{2}{3}$ chance of not throwing $5$ or $6$.
For four throws of dice, the chance of not rolling $5$ or $6$ is then $\frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}\times \frac{2}{3}=\frac{16}{81}$
Probability that you will through $5$ or $6$ atleast once $=\frac{81-16}{81}=\frac{65}{81}$