In Exercises 11–16, a die is rolled. Find the probability of getting a 4.

Verified step by step guidance

1. Understand that a standard die has 6 faces, numbered from 1 to 6, and each face has an equal chance of landing face up.
2. Identify the total number of possible outcomes when rolling the die, which is 6.
3. Determine the number of favorable outcomes for the event 'getting a 4', which is 1 (only the face with the number 4).
4. Use the probability formula: $P=\frac{\mathrm{Number} \mathrm{of} \mathrm{favorable} \mathrm{outcomes}}{\mathrm{Total}}$.
5. Substitute the values into the formula: $P=\frac{1}{6}$.
6. Interpret the result as the probability of rolling a 4 on a single roll of the die.

Key Concepts

Sample Space

The sample space is the set of all possible outcomes of an experiment. For a single roll of a standard die, the sample space consists of six outcomes: {1, 2, 3, 4, 5, 6}. Understanding the sample space is essential to calculate probabilities accurately.

Event

An event is a specific outcome or a set of outcomes from the sample space. In this question, the event is rolling a 4, which is one specific outcome. Identifying the event helps in determining the favorable outcomes for the probability calculation.

Probability Formula

Probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes. For rolling a 4 on a die, the probability is 1 (favorable outcome) divided by 6 (total outcomes), resulting in 1/6. This formula is fundamental for solving probability problems.