When you roll a pair of fair six

Step by Step Solution

Part (a) Step 1: Given information

Given in the question that , roll a pair of fair, six-sided dice. Let = the sum of the spots showing on the up-faces

We need to find the probability distribution of

Part (a) Step 2: Explanation

sum of spots on a roll of a pair of fair, six-sided dice.

Each die has 6 possible outcomes:

Let us next determine all possible sums when rolling a pair of six-sided dice:

Part (a) Step 3: Probability 

Part (b) Step 1: Given information

Given in the question that , roll a pair of fair, six-sided dice. Let = the sum of the spots showing on the up-faces.

We need to make a histogram of the probability distribution.

Part (b) Step 2: Explanation

From (a) part of the question

Each bar's width must be equal, and its height must be equal to the probability:

Part (c) Step 1: Given information

Given in the question that, u roll a pair of fair, six-sided dice. Let = the sum of the spots showing on the up-faces.

We need to find

Part (c) Step 2: Explanation

From part (a)

For discontinuous or mutually exclusive occurrences, use the following addition rule:

Because it is impossible to toss to two distinct sums for the same rolls, the events are mutually exclusive, and the addition rule is applicable for mutually exclusive occurrences:

What is the probability of rolling a 6 with a pair of dice?

Is rolling a 6 on a 6 sided dice likely to happen?

Are 6 sided dice fair or unfair?

What is a fair 6 sided dice?