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Homework 3 MAT350 1. Two fair dice are rolled and X denotes the absolute value of the difference of the outcomes. What are the possible values of X, and the probabilities associated with them? 2. In a small town there are 40 taxis, numbered 1 to 40. Three taxis arrive at random at a station to pick up passengers. What is the probability that the number of at least one of the taxis is less than 5? 3. Suppose that jury members secede independently and that each with probability p (0<p<1) makes the correct decision. If the decision of the majority is final, which is preferable: a three-man jury or a single juror? 4. From an ordinary deck of 52 cards, cards are drawn at random and with replacement. What is the probability that, of the first eight cards drawn, four are spades? 5. a graduate class consists of six students. What is the probability that exactly three of them are born either in April or October? 6. A manufacturer of nails claims that only 3% of his nails are defective. A random sample of 24 nails is selected, and it is found that two of them are defective. Is it fair to reject the manufacturer’s claim based on this observation? 7. Jim buys 60 lottery tickets every week. If only 5% of the lottery tickets win, what is the probability that he wins next week? 8. Suppose that 2.5% of the population of a border town are illegal immigrants. Find the probability that, in a theater of this town with 80 random viewers, there are at least two illegal immigrants. 9. From an ordinary deck of 52 cards we draw cards at random, with replacement, and successively until an ace is drawn. What is the probability that at lest 10 draws are needed? Page 1 of 2 Homework 3 MAT350 10. The probability is p that a randomly chosen light bulb is defective. We screw a bulb into a lamp and switch on the current. If the bulb works, we stop; otherwise, we try another and continue until a good bulb is found. What is the probability that at least n bulbs are required? 11. On average, how many games of bridge are necessary before a player is dealt three aces? A bridge hand is 13 randomly selected cards from an ordinary deck of 52 cards. 12. A restaurant serves 8 fish entrées 12 beef, and 10 poultry. If customers select from these entrées randomly, what is the expected number of fish entrées ordered by the next four customers? 13. A doctor has five patients with migraine headaches. He prescribes for all five a drug that relieves the headaches of 82% of such patents. What is the probability that the medicine will not relieve the headaches of two of these patients? 14. The policy of the quality control division of certain corporation is to reject a shipment if more than 5% of its items are defective. A shipment of 500 items is received, 30 of them are randomly tested, and two have been found defective. Should that shipment be rejected? Page 2 of 2