An experiment consists of rolling two fair dice and adding...

An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Using the sample space shown in Figure 1 (p. 929 ) and assuming each simple event is as likely as any other, find the probabilities of the sums of dots indicated.

Sum is divisible by 4

Key Concepts

Divisibility Rule

Divisibility rules are used to determine if a number can be evenly divided by another number without a remainder. In probability problems, such rules help to define events based on numerical properties, such as sums that are divisible by a given number.

Probability Event

An event is a specific subset of outcomes from the sample space that share a common property, such as having a sum divisible by a particular number. Understanding what constitutes an event allows one to identify and count the relevant outcomes when calculating probablity.

Fundamental Counting Principle

This principle states that the total number of outcomes of a compound experiment is the product of the number of outcomes for each individual experiment. For instance, when rolling multiple dice, you multiply the number of outcomes for each die to find the total number of outcomes in the sample space.

Equally Likely Outcomes

This concept means that each outcome in the sample space has an equal chance of occurring. When dealing with fair dice, each face and the resulting pair of outcomes are assumed to have the same probability, which simplifies the calculation of probabilities.

Sample Space

The sample space is the complete set of all possible outcomes of an experiment. In probability, defining the sample space is essential because it provides the basis for calculating probabilities by considering every possible outcome.

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