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

Verified step by step guidance

1. Identify the total number of possible outcomes when rolling a standard die. Since a die has 6 faces, the total number of outcomes is 6.
2. Determine the favorable outcomes for the event 'getting a number greater than 4.' The numbers greater than 4 on a die are 5 and 6.
3. Count the number of favorable outcomes. There are 2 numbers greater than 4 (5 and 6), so the number of favorable outcomes is 2.
4. Use the probability formula: $P=\frac{\mathrm{Number} \mathrm{of} \mathrm{favorable} \mathrm{outcomes}}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{possible} \mathrm{outcomes}}$.
5. Substitute the values into the formula: $P=\frac{2}{6}$. This fraction can be simplified if needed.

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 the numbers {1, 2, 3, 4, 5, 6}. Understanding the sample space is essential to determine the total number of possible outcomes.

Event and Favorable Outcomes

An event is a subset of the sample space that satisfies a given condition. In this problem, the event is rolling a number greater than 4, which includes the outcomes {5, 6}. Identifying favorable outcomes helps in calculating the probability of the event.

Probability Calculation

Probability is calculated as the ratio of favorable outcomes to the total number of possible outcomes. For a fair die, each outcome is equally likely, so the probability of rolling a number greater than 4 is the number of favorable outcomes divided by the total outcomes, i.e., 2/6 or 1/3.