Two fair dice are rolled (see Figure 10.16 ). What is the probability of a. a sum less than four

step 1 Okay, so this problem has given us a situation where two fair dice are rolled. And it says C fig

Two fair dice are rolled (see Figure 10.16 ). What is the...

Key Concepts

Favorable Outcomes

Favorable outcomes refer to the specific outcomes in the sample space that satisfy the event criteria. In probability problems, determining the number of favorable outcomes is essential for computing the probability of events.

Uniform Probability Distribution

A uniform probability distribution assumes that each outcome in the sample space is equally likely. When dealing with fair dice, this concept allows us to calculate the probability of an event by dividing the number of favorable outcomes by the total number of outcomes.

Complement Rule

The complement rule is a technique used in probability to find the probability that an event does not occur by subtracting the probability of the event from one. This is particularly useful for events where directly counting the favorable outcomes for the complement is easier than counting them for the event itself.

Sample Space

The sample space is the collection of all possible outcomes for a probabilistic experiment. In the context of rolling two dice, it involves considering every pair of numbers that could appear, which forms the basis for calculating probabilities by counting outcomes.

Counting Principle

The counting principle is used to determine the total number of outcomes by multiplying the number of outcomes for each independent event. For rolling two dice, this principle helps in computing that there are a fixed number of equally likely outcomes.

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