Mike owns a box that contains 6 pairs of 14-carat gold, cubic zirconiaearrings. The earrings are of three sizes: 3mm, 4mm, and 5mm. Thereare 2 pairs of each size.Each time that Mike needs an...

Mike owns a box that contains 6 pairs of 14-carat gold, cubic zirconia earrings. The earrings are of three sizes: 3mm, 4mm, and 5mm. There are 2 pairs of each size. Each time that Mike needs an inexpensive gift for a female friend, he randomly selects a pair of earrings from the box. If the selected pair is 4mm, then he buys an identical pair to replace it. If the selected pair is 3mm, then he does not replace it. If the selected pair is 5mm, then he tosses a fair coin. If he observes Heads, then he buys two identical pairs of earrings to replace the selected pair; if he observes Tails, then he does not replace the selected pair. (a) What is the probability that the second pair selected will be 4mm? (b) If the second pair was not 4mm, then what is the probability that the first pair was 5mm?