# Homework 3 MAT350 1. Two fair dice are rolled and X denotes the

```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&lt;p&lt;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
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?
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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 entr&eacute;es 12 beef, and 10 poultry. If customers select
from these entr&eacute;es randomly, what is the expected number of fish entr&eacute;es 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?
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