Probabilities with Two-Way Tables

Place 6 balls that are neither striped nor spotted into the container along with 5 spotted and striped balls. Are the events of selecting a spotted ball and selecting a striped ball dependent or independent? Why?

Place 2 spotted striped balls, 3 striped but not spotted balls, 4 spotted but not striped balls, and 6 balls that are neither striped nor spotted into the container.  Are the events of selecting a spotted ball and selecting a striped ball dependent or independent? Why?

Can you add a different selection of balls to the container so that events A and B are independent? Describe your strategy.

Set up a scenario where P(A) is equal to P(A|B).  What happens if you remove an object from the collection?  Are A and B still independent events?  Will this be true no matter which object you remove?  Why or why not?

If P(A) = P(A|B), is it possible that P(B) is not equal to P(B|A)? Why or why not?

The multiplication rule for probability states that P(A and B)=P(A)P(B|A). If A and B are independent events, how could you determine P(A and B) if you knew P(A) and P(B)?