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.

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. In the context of rolling a die, the probability of any specific outcome (like rolling a 2) is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For a fair six-sided die, the probability of rolling a specific number is 1/6.

Two events are considered independent if the occurrence of one does not affect the occurrence of the other. In this scenario, rolling a die twice involves independent events, meaning the result of the first roll does not influence the result of the second roll. This independence allows us to multiply the probabilities of each individual event to find the overall probability.

The multiplication rule states that the probability of two independent events both occurring is the product of their individual probabilities. For the given problem, to find the probability of rolling a 2 first and then a 3, you multiply the probability of rolling a 2 (1/6) by the probability of rolling a 3 (1/6), resulting in a combined probability of 1/36.