Question

Your parents allow you to have an outing with your friends every Saturday of the month. You select the movies, bowling, skating, and the arcade as your activities for this month and put them on slips of paper in a jar to randomly select. In 3-5 sentences, describe the independent and dependent probabilities, then determine how many possible events you could have for the month if the movie outing is selected first and not replaced. Answer in paragraph form.

Answer 1

In this scenario, the independent probabilities refer to the selection of activities since each additional selection is based on the previous one. The first activity selected, such as movies, does not affect the probability of the subsequent choices, but the dependent probabilities come into play when considering the remaining activities after the first selection since it alters the available options. If the movie outing is selected first and not replaced, there are three remaining activities left in the jar: bowling, skating, and the arcade. For each of these subsequent outings, you would choose from the remaining options, leading to calculated combinations. Therefore, the total number of possible events for the month, starting with the movie, is 3! (3 factorial), which equals 6 different sequences of the remaining activities.