Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it.
(a) What is the probability that the first marble you draw is blue?
(b) Suppose you drew a blue marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw?
(c) Suppose you instead drew an orange marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw?
(d) If drawing with replacement, what is the probability of drawing two blue marbles in a row?
(e) When drawing with replacement, are the draws independent? Explain.