Question

If the die is rolled $300$ times, how many times would you predict a roll of a $1$ or a $6$?

Answer 1

Find probability of getting $1$or a $6$, if the die is rolled $300$ times.

The ratio of the number of favorable outcomes to the total number of outcomes of an event is called Probability.

$\text{Probability P}\left(A\right)=\frac{\text{favorable outcomes n}\left(A\right)}{\text{Total outcomes n}\left(S\right)}$.

Possible outcomes $\left(S\right)=\left\{1,2,3,4,5,6\right\}$

Total outcomes $n\left(S\right)=6$

favorable outcomes $\left(A\right)=\left\{1,6\right\}$

Number of favorable outcomes $n\left(A\right)=2$

So,

$\begin{array}{rcl}P\left(A\right)& =& \frac{n\left(A\right)}{n\left(S\right)}\\ & =& \frac{2}{6}\\ & =& \frac{1}{3}\end{array}$

Probability of getting a $1$ or a $6$ is $\frac{1}{3}$.

The die is rolled $300$ times, So multiply probability by $300$.

$\frac{1}{3}\times 300=100$

Therefore, the probability of getting $1$or a $6$, if the die is rolled $300$ times is $100$.