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An urn contains two green balls and three red balls. Suppose two balls will be drawn at random one after another and without replacement (i.e., the first ball drawn is not returned to the urn before the second one is drawn).

(a) Find the probabilities of the events

A = [ Green ball appears in the first draw ]

B = [ Green ball appears in the second draw ]

(b) Are the two events independent? Why or why not?

(c) Now suppose two balls will be drawn with replacement (i.e., the first ball drawn will be returned to the urn before the second draw). Repeat parts (a) and (b).