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: