Question

Question: What is the variance of the number of times a 6 appears when a fair die is rolled 10 times?

Short answer

Answer:So, the expected value of the random variable is: \(\frac{{25}}{{18}}\)

Step-by-step solution

Given data

A fair die is rolled \(10\)times.

Definition

The term variance refers to a statistical measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean and thus from every other numbers in the set.

Calculation

Here, the variance of the number of successes in\(n\)Bernoulli trial is\(npq\)where\(n\)is the number of tries,\(p\)is the success probability and\(q\)is the fail probability.

As we see in the question a success is get when we get a \(6\)on the dice with probability \(p = \frac{1}{6}\).

Final step 

Hence, the variance is\(\begin{array}{l}q = 1 - \frac{1}{6}\\q = \frac{5}{6}\end{array}\)

So, we throw the dice\(10\)times.

Hence, the variable is\(10 \times \frac{1}{6} \times \frac{5}{6} = \frac{{25}}{{18}}\).