Question

David rolled a number cube 20 times. The cube landed on the number 3 six times. Which best describes what would likely happen if Dan rolled the number cube another 80 times?

Answer 1

Answer:

It is likely that the experimental probability of 3 will reach towards the theoretical probability of 3, if Dan rolled the number cube another 80 times.

Step-by-step explanation:

A number cube has 6 faces and contains the numbers from 1 to 6 on each of its faces.

And each number is equally likely to come.

i.e. Theoretical probability of each face = $\frac{1}{6}$

Probability of any event E is given as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

It is given that number of times 3 occurs is 6 out of 20.

So, experimental probability of 3 = $\frac{6}{20}=\frac{3}{10}$

Here, we can see that experimental probability of 3 is greater than that of theoretical probability of 3.

But the number of iterations here are smaller in number i.e. only 20.

As the number of iterations will increase, it is likely that the experimental probability of 3 will reach towards the theoretical probability of 3.

So, we can say that:

It is likely that the experimental probability of 3 will reach towards the theoretical probability of 3, if Dan rolled the number cube another 80 times.