Question

A fair, six-sided die is rolled ten times. Each roll is independent. You want to find the probability of rolling a one more than three times. State the probability question mathematically.

Short answer

The probability question is stated mathematically as to find$P(X>3)$

Step-by-step solution

Content Introduction

We are given,

A fair, six-sided die is rolled ten times.

Each roll is independent

Content Explanation

Here the random variable, $X=$number of times the fair six-sided die roll the number one out of ten times rolled independently.

Then the assumed values of $X=0,1,2,3,....,10.$

The probability that the fair six-sided die rolls the number one in one rolling is $p=\frac{1}{6}$

The probability that the fair six-sided die does not rolls the number one in one rolling $q=\frac{5}{6}$

The number of times of fair six sided die is rolled is $n=10$

It is to find the probability of rolling a number one on fair six-sided die more than three times.

Therefore, the probability question is stated mathematically as to find$P(X>3)$.