In Exercises 49–52, a single die is rolled twice. Find the probability of rolling a 2 the first time and a 3 the second time.

Verified step by step guidance

1. Understand that the problem involves two independent events: rolling a die twice, where the outcome of the first roll does not affect the second roll.
2. Recall that the probability of rolling any specific number on a fair six-sided die is \( \frac{1}{6} \).
3. Calculate the probability of rolling a 2 on the first roll, which is \( \frac{1}{6} \).
4. Calculate the probability of rolling a 3 on the second roll, which is also \( \frac{1}{6} \).
5. Since the rolls are independent, multiply the probabilities of the two events: \( \frac{1}{6} \times \frac{1}{6} \) to find the combined probability.

Key Concepts

Probability of a Single Event

The probability of a single event is the likelihood that the event will occur, calculated as the number of favorable outcomes divided by the total number of possible outcomes. For a fair six-sided die, the probability of rolling any specific number, like a 2, is 1/6.

Independent Events

Two events are independent if the outcome of one does not affect the outcome of the other. Rolling a die twice produces independent events because the result of the first roll does not influence the second roll.

Multiplication Rule for Independent Events

When two events are independent, the probability of both occurring is the product of their individual probabilities. For example, the probability of rolling a 2 first and a 3 second is (1/6) × (1/6) = 1/36.