Question

An eight-sided dice numberedfrom 1 to 8 is rolled 80 times todetermine whether it is fair,a If the dice is fair, how manyof each number would you expect to get?

Answer 1

We were given the following information:

The dice is 8-sided, numbered from 1-8

We are to decide if the dice is fair. We do this as shown below:

$\begin{gathered} \text{For a fair dice, we have:} \\ P=\frac{Favourable\text{ Outcome}}{Total\text{ Outcome}} \\ P\mleft(1\mright)=\frac{1}{8} \\ P(2)=\frac{1}{8} \\ P(3)=\frac{1}{8} \\ P(4)=\frac{1}{8} \\ P(5)=\frac{1}{8} \\ P(6)=\frac{1}{8} \\ P(7)=\frac{1}{8} \\ P(8)=\frac{1}{8} \end{gathered}$

If the dice is rolled 80 times, we expect the answer to be as shown below:

$\begin{gathered} P(1)=\frac{1}{8}\times80=10 \\ P(2)=\frac{1}{8}\times80=10 \\ P(3)=\frac{1}{8}\times80=10 \\ P(4)=\frac{1}{8}\times80=10 \\ P(1)=\frac{1}{8}\times80=10 \\ P(1)=\frac{1}{8}\times80=10 \\ P(1)=\frac{1}{8}\times80=10 \\ P(1)=\frac{1}{8}\times80=10 \end{gathered}$

Therefore, for a fair dice, we would get each number: 10 times