In Exercises 49–52, a single die is rolled twice. Find the probability of rolling an even number the first time and a number greater than 2 the second time.

Verified step by step guidance

1. Step 1: Identify the sample space for a single die roll, which is {1, 2, 3, 4, 5, 6}.
2. Step 2: Determine the probability of rolling an even number on the first roll. The even numbers on a die are {2, 4, 6}.
3. Step 3: Calculate the probability of rolling an even number on the first roll, which is the number of favorable outcomes (3) divided by the total number of outcomes (6).
4. Step 4: Determine the probability of rolling a number greater than 2 on the second roll. The numbers greater than 2 are {3, 4, 5, 6}.
5. Step 5: Calculate the probability of rolling a number greater than 2 on the second roll, which is the number of favorable outcomes (4) divided by the total number of outcomes (6). Multiply the probabilities from Step 3 and Step 5 to find the combined probability.

Key Concepts

Probability Basics

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. In this context, it involves calculating the chances of specific outcomes when rolling a die. Understanding how to determine the total number of possible outcomes is crucial for calculating probabilities.

Independent Events

In probability, independent events are those whose outcomes do not affect each other. When rolling a die twice, the result of the first roll does not influence the second roll. This concept is essential for calculating the combined probability of multiple events occurring in sequence.

Event Outcomes

Identifying the specific outcomes of interest is key to solving probability problems. In this case, the first event is rolling an even number (2, 4, or 6), and the second event is rolling a number greater than 2 (3, 4, 5, or 6). Understanding how to count these favorable outcomes relative to the total possible outcomes is necessary for accurate probability calculation.