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 2 on the first roll and rolling a 3 on the second roll of a single die.
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 two rolls are independent, multiply the probabilities of each event to find the combined probability: \(\frac{1}{6} \times \frac{1}{6}\).

Key Concepts

Probability of a Single Event

Probability measures the likelihood of an event occurring, calculated as the ratio of favorable outcomes to total 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 involves independent events because the result of the first roll does not influence the second.

Multiplication Rule for Independent Events

When two events are independent, the probability of both occurring is the product of their individual probabilities. To find the chance of rolling a 2 first and a 3 second, multiply 1/6 by 1/6, resulting in 1/36.