In Exercises 11–16, a die is rolled. Find the probability of getting an odd number.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. An event with a probability of 0 will not happen, while an event with a probability of 1 is certain to occur. In this context, we are interested in the probability of rolling an odd number on a die.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For a standard six-sided die, the sample space consists of the numbers {1, 2, 3, 4, 5, 6}. Understanding the sample space is crucial for calculating probabilities, as it provides the total number of outcomes against which specific events can be measured.

Favorable Outcomes

Favorable outcomes are the specific outcomes in the sample space that satisfy the condition of the event we are interested in. In this case, the favorable outcomes for rolling an odd number are {1, 3, 5}. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space.