Question

If you roll two number cubes 100 times, about how many times can you expect the product to be a multiple of 6? (Example 6, 12, 18, ect) (make a table) Provide mathematical evidence to support your answer.

Answer 1

Using the binomial distribution, it is found that you could expect the product to be a multiple of 6 about 39 times.

For each trial, there are only two possible outcomes, either the result is a multiple of 6, or it is not. The result of each trial is independent of any other trial, hence the binomial distribution is used to solve this question.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

$E(X) = np$

In this problem:

• When two cubes are tossed and their products multiplied, there are 36 possible outcomes. Of those, (1,6), (2,3), (2,6), (3,4), (3,6), (4,3), (4,6), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6), that is, 14 result in a multiplication multiple of 6, hence p = 14/36.

• There will be 100 trials, hence n = 100.

Then, the expected value is given by:

$E(X) = np = 100 \times \frac{14}{36} = 38.89$

Rounding up, you could expect the product to be a multiple of 6 about 39 times.

More can be learned about the binomial distribution at brainly.com/question/24863377