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 1

In this scenario, the independent probability refers to the selection of the first activity (e.g., movies), which doesn't rely on any other activity being chosen beforehand. The dependent probability comes into play when considering the subsequent activities, since the selection of one option affects the available choices for the remaining outings. If you have four activities (movies, bowling, skating, and the arcade) and you select movies first without replacement, then you are left with three remaining activities to choose from for the next outings.

Since there are a total of 4 activities and if you select movies first, the number of possible events for the month with the remaining three activities is calculated by finding the permutations of the remaining activities. So you would have 3! (3 factorial), which equals 6 different ways to arrange the remaining activities. Thus, the total number of possible events for the month would be \(6\) arrangements after the first selection of movies.