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)

Answer 1

To determine if the events you are drawing are independent or dependent probabilities, you need to follow these steps:

1. Define Events: Clearly define the events you are interested in. For example, let \( A \) be the event of drawing "movies" and \( B \) be the event of drawing "bowling".

2. Understand Independence: Remember that two events are independent if the occurrence of one event does not affect the probability of the other event occurring. Mathematically, this means \( P(A \cap B) = P(A) \times P(B) \).

3. Perform Trials: Conduct experiments where you draw activities for the four Saturdays. After each selection, note the activities and whether you replace the drawn slip back into the cup or keep it out (affecting subsequent draws). This will affect whether the probabilities are independent or dependent.

4. Calculate Probabilities:

   • If you replace the slip after each draw, each draw remains independent. Calculate the probabilities of drawing each activity and the joint probabilities.
   • If you do not replace the slip, the outcomes of the first draws will affect the probabilities of later draws, making them dependent.

5. Evaluate Results: Analyze the recorded outcomes and computed probabilities to determine if they fit the criteria of independence or dependency.

By following these steps, you will be able to conclude whether the events drawn from your cup are independent or dependent based on the method you choose for drawing.