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)
Answers
GPT-4o mini
In this scenario, the independent probability refers to the likelihood of selecting a specific activity (like bowling, skating, or the arcade) after the first activity (the movie outing) has been chosen. The dependent probability, on the other hand, pertains to the likelihood of selecting one of the remaining activities after one has already been chosen, as the pool of options decreases with each selection.
Since the movie outing is selected first and is not replaced, this leaves 3 remaining activities (bowling, skating, and the arcade) for the subsequent outings. Thus, there are 3 possible activities left for choice on the second outing, and then 2 activities left for choice on the third outing, leaving 1 activity available for the fourth outing. Consequently, the total number of possible events for the month, given that the movie is selected first, is calculated as follows: 3 (second outing) × 2 (third outing) × 1 (fourth outing) = 6 possible events.
Since the movie outing is selected first and is not replaced, this leaves 3 remaining activities (bowling, skating, and the arcade) for the subsequent outings. Thus, there are 3 possible activities left for choice on the second outing, and then 2 activities left for choice on the third outing, leaving 1 activity available for the fourth outing. Consequently, the total number of possible events for the month, given that the movie is selected first, is calculated as follows: 3 (second outing) × 2 (third outing) × 1 (fourth outing) = 6 possible events.