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

Verified step by step guidance

1. Identify the total number of possible outcomes when rolling a die. Since a standard die has 6 faces, the total number of outcomes is 6.
2. Determine the favorable outcomes for the event 'getting an odd number.' The odd numbers on a die are 1, 3, and 5, so there are 3 favorable outcomes.
3. Recall the formula for probability: $P\left(E\right)=\frac{\mathrm{Number} \mathrm{of} \mathrm{favorable} \mathrm{outcomes}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{possible} \mathrm{outcomes}}$.
4. Substitute the values into the probability formula: $P\left(\mathrm{odd}\right)=\frac{3}{6}$.
5. Simplify the fraction if possible to express the probability in simplest form.

Key Concepts

Sample Space

The sample space is the set of all possible outcomes of an experiment. For a single roll of a die, the sample space consists of the numbers 1 through 6, representing each face of the die.

Event

An event is a subset of the sample space that includes outcomes of interest. In this problem, the event is rolling an odd number, which includes the outcomes {1, 3, 5}.

Probability Calculation

Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. Here, the probability of rolling an odd number is the number of odd outcomes divided by 6.