Part One: Probability

Case Study #1.12:

Conditional Probability II: Pair'O'Dice

Case Description: Compute conditional probabilities.

Suppose we have a pair of fair dice: d4(faces 1,2,3,4), d6(faces 1,2,3,4,5,6). In our experiment, we toss this pair of dice, and note the face value from each die. For simplicity, we write the outcome as (d4 result, d6 result). Assume that the dice operate independently and separately.

Case Objectives:

Identify the simple (basic) events. Compute (and justify) a probability for each simple event. 

Suppose we observe the sum of the faces in the pair of dice. Identify the possible values of this sum, and compute (and justify) a probability for each value.

Compute the conditional probability Pr{Sum is Even|d4 shows Even}.

Compute the conditional probability Pr{Sum is Odd|d6 shows Odd}.