Let S be the set of outcomes when two distinguishable dice...

Let $S$ be the set of outcomes when two distinguishable dice are rolled, let $E$ be the subset of outcomes in which at least one die shows an even number, and let $F$ be the subset of outcomes in which at least one die shows an odd number. List the elements in each subset given. $$ (E \cup F) $$

Key Concepts

Distinguishable Dice

When dice are distinguishable, each die is treated as a unique object, meaning that the outcome (a, b) is considered different from (b, a). This is a critical point in forming the sample space and in the analysis of events since it affects the total number of outcomes.

Union of Events

The union of events, denoted E ? F, is a set that contains all outcomes that belong to either event E or event F (or both). In probability, forming unions of events helps in understanding scenarios where multiple conditions may be satisfied simultaneously.

Even and Odd Classification

This key concept involves categorizing numbers based on their divisibility by 2. Even numbers are integers divisible by 2, while odd numbers are not. These classifications are used in the events described in the problem to determine which outcomes are included in events E and F.

Sample Space

The sample space is the set of all possible outcomes of an experiment. In this context, it refers to all ordered pairs that can result from rolling two distinguishable dice, where the order matters because the dice are different.

Events in Probability

An event is a subset of the sample space that consists of outcomes satisfying a specific condition. Here, events such as E and F are defined by whether the outcomes contain at least one even number or at least one odd number, respectively.

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