Consider a jar that contains 10 balls, 6 of which are purple.

a. If you pick just one ball, what is the probability that it is purple?

b. If you randomly pick two balls where you replace the first ball before picking the second (i.e., the drawing is 'with replacement'), what is the probability of them both being purple? (Show and explain your calculation.)

c. If you randomly pick two balls where you do not replace the first ball before picking the second (i.e., the drawing is 'without replacement'), what is the probability of them both being purple? (Show and explain your calculation.)

d. Let E be the event that the first ball is purple and F be the event that the second ball is purple. For which of the two situations, drawing with replacement or drawing without replacement, are the events E and F independent. Explain your answer.