As a reward for your good grades, you are allowed to have an outing with your friends for the next 4 Saturdays. In order to choose what you are going to do, you made a list of activities: the movies, bowling, skating and the arcade. You put them on separate slips of paper and put them in a cup to randomly select.

Question

Question 1
What would you need to do as your are drawing events to determine if they are independent or dependent probabilities?(1 point)
0 / 10000 Word Limit
Question 2
If bowling is picked as the first activity, how many permutations are possible for the remaining events? List all the possibilites(2 points)

Answer 1

Question 1

To determine if the events of selecting activities for each of the Saturdays are independent or dependent probabilities, you would need to observe how the selection of one activity affects the selection of another. Specifically, you would:

1. Draw the first activity from the cup and note it down.
2. Without replacing the first slip back into the cup, draw the second activity.
3. Note whether the first drawing affects your choices for the second activity.
4. Repeat this process for all four Saturdays, assessing at each step whether the remaining choices are influenced by past selections.

If drawing one activity changes the outcomes available for subsequent selections, the events are dependent. If every selection is unaffected by the previous draws (which would require replacement), the events are independent.

Question 2

If bowling is picked as the first activity, there are three remaining activities: the movies, skating, and the arcade. The number of permutations of these three activities can be calculated as 3!, which is 3 factorial.

3! = 3 × 2 × 1 = 6 permutations.

The possible arrangements of the remaining activities following bowling are:

1. Bowling, Movies, Skating, Arcade
2. Bowling, Movies, Arcade, Skating
3. Bowling, Skating, Movies, Arcade
4. Bowling, Skating, Arcade, Movies
5. Bowling, Arcade, Movies, Skating
6. Bowling, Arcade, Skating, Movies

Thus, those are the six possible permutations for the remaining events after selecting bowling first.