In this scenario, the independent events are the individual activities selected for each Saturday, as each choice does not affect the remaining options for subsequent Saturdays. The dependent probability comes into play when an activity is selected and not replaced; this alters the pool of remaining options for subsequent selections. Since there are four activities (movies, bowling, skating, and the arcade) and one will be chosen first, the number of possible events for the month is calculated by considering the selection process without replacement. After selecting the movie first, three activities remain, leading to the following combinations for the remaining Saturdays: 3 (for the second Saturday) × 2 (for the third Saturday) × 1 (for the fourth Saturday) = 6 possible unique arrangements for the month after the movie is selected first.
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.
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