6. (8 Marks) The game of “odd man out” is played with 3 people, each ipping a single coin. All 3
ip their coin simultaneously; if one face is dierent from the other two, its owner is the odd man
and he loses.
(a) (4 Marks) What is the probability that there is an odd man on a given turn, assuming all
three coins are fair?
(b) (4 Marks) If there is no odd man on the rst turn, the coins are all ipped again, until the
odd man is determined. What is the probability that an even number of turns is required to
determine the loser?
7. (5 Marks) We have two coins; the rst is fair and the second is two-headed. We pick one of the
coins at random, we toss it twice and heads show both times. Find the probability that the coin
picked was fair.
8. (6 Marks) A company producing electric relays has three manufacturing plants producing 50,
30, and 20 percent, respectively, of its product. Suppose that the probabilities that a relay
manufactured by these plants is defective are 0:02; 0:05; and0:01, respectively.
(a) (3 Marks) If a relay is selected at random from the output of the company, what is the
probability that it is defective?
(b) (3 Marks) If a relay selected at random is found to be defective, what is the probability that
it was manufactured by plant 2?
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