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Unformatted text preview: / 1. Five cars start out on a crosscountry race. The probability
that a car breaks down and drops out of the race is 0.2 . What
is the probability that at least 3 cars finish the race? 2. We have two dice, A and 8. Die A has 4 Red and 2 White
faces and Die B has 2,Red and 4 White faces. We will play a game
by first choosing a die; die A is selected with probability p.
The chosen die is tossed until a White face appears, at which
time the game is ended. . After playing the game a great many times, it is observed
that the probability that a game ends in exactly 3 tosses of the
selected die is 7/81. Determine the value of p. 3. A biased coin has a probability p of coming up Heads when
tossed. It is tossed 6 times by your friend who tells you that
Heads turned up in more than half of the tosses. Given that information. what is the probability that Heads appeared in all 6
of the tosses? 4. In the figure below, the notation __4J___ represents a
communication link. Link failures are indepen ent, and each link
has a probability of 0.5 of being out of service. Towns A and B
'can communicate as long as they are connected by at least one
communication path which contains only inservice links. In an
efficient manner, determine the probability that A and B can
communicate. 5. A pair of foursided dice is thrown once. Each.die has faces
labeled 1,2,3,and 4. The discrete random variable X is defined
‘to be the product of the downface values. Determine the
conditional variance of x‘ given that the sum of the downface
values is greater than the product of the downface values. ./é. A computer will fail in its kth month of use with probability
—l
" J. 4  ' ~§
Pk " 6 : “1.13, ' . J
Four computers are lifetested simultaneously. Find ' the probability that:
a) None of the four computers fails during its first month of use.
b) Exactly two computers have failed by the end of the third month.
c) Exactly one'computer fails during each of the first three months.
d) Exactly one computer has failed by the end of the second month, and exactly two computers are still working at 7. a) A wheel of fortune is spun three times. What is the
probability that none of the resulting spins is within 30 degrees of any other spin?
b) What is the smallest number of spins for which the probability that at least one other reading is within plus or
minus 30 degrees of the first reading is at least 0.9 ? ’//E.The probability that a store will have exactly k customers on
any given day is ﬁt
\123 ‘é (€g3 ‘2‘“°:U b‘“ On each day when the store has had at least one customer, one of
the sales slips is selected at random and a door prize is mailed
to the corresponding customer. (Each sales slip corresponds to a unique customer, and each customer buys exactly one item).
a) What is the probability that a customer selected randomly from the population of all customers will win a door prize?
b) Given a customer who has won a door prize, what is the
probability that he was in the store on a day when it had exactly K‘customers? P=oQ
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 Spring '09
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 Probability, Dice, heads, door prize, Hm uuuw ma

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