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.(4 points)

Answer 1

In this scenario, the independent probability refers to the likelihood of choosing a specific activity (like going to the movies) independently of any previous choices. The dependent probability, on the other hand, is the probability of selecting an activity influenced by previous selections, as in this case, if a movie is chosen first and not replaced, the remaining choices for the next outings are affected.

Assuming there are four activities (movies, bowling, skating, and the arcade), if the movie outing is selected first and not replaced, you will have three activities left to choose from for the remaining outings. Since there are four Saturdays in the month, you can calculate the possible outcomes as follows: after selecting the movie first, there are \(3\) choices remaining for the second Saturday, \(2\) choices for the third Saturday, and \(1\) choice for the last Saturday. Thus, the total number of possible combinations of activities for the month would be \(3 \times 2 \times 1 = 6\).