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

Verified step by step guidance

1. Step 1: Understand the problem. We need to find the probability of rolling a number greater than 4 on a standard six-sided die.
2. Step 2: Identify the possible outcomes when a die is rolled. A standard die has six faces, numbered 1 through 6.
3. Step 3: Determine the favorable outcomes. The numbers greater than 4 on a die are 5 and 6.
4. Step 4: Count the number of favorable outcomes. There are 2 numbers (5 and 6) that are greater than 4.
5. Step 5: Calculate the probability. The probability is the number of favorable outcomes divided by the total number of possible outcomes, which is 6.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it quantifies the chance of rolling a number greater than 4 on a standard six-sided die. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.

Sample Space

The sample space is the set of all possible outcomes of a random experiment. For a single roll of a 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 context for determining favorable outcomes.

Favorable Outcomes

Favorable outcomes are the specific results of an experiment that satisfy the condition of interest. In this case, the favorable outcomes for rolling a number greater than 4 are the numbers 5 and 6. Identifying these outcomes is essential for calculating the probability of the event occurring.