Question

Look at the question & write your answer for ABC

Answer 1

Solution:

From the given table;

The total possible outcome is 500

The even numbers are 2, 4 and 6.

Their experimental probabilities are

$\begin{gathered} P(2)=\frac{84}{500} \\ P(4)=\frac{81}{500} \\ P(6)=\frac{89}{500} \end{gathered}$

a) The experimental probability of rolling an even number is

$\begin{gathered} P(even)=\frac{84}{500}+\frac{81}{500}+\frac{89}{500} \\ P(even)=\frac{84+81+89}{500}=\frac{254}{500}=\frac{127}{250} \\ P(even)=\frac{127}{250} \end{gathered}$

Hence, the experimental probability of rolling an even number is 127/250

b) Assuming the cube is fair,

The even numbers are 2. 4 and 6

$nP(even)=3$

The total possible outcome is 6

The theoretical probability of rolling an even number is

$\begin{gathered} P(even)=\frac{3}{6}=\frac{1}{2} \\ P(even)=\frac{1}{2} \end{gathered}$

Hence, the theoretical probability of rolling an even number is 1/2

c) Assuming the cube is fair,

The larger the number of rolls, the greater the likelihood that the experimental probability will be close to the theoretical probability