CHAPTER 6 REVIEW
1. In the followina
D E
A
15 12
B
15 23
C
32 28
TOTAL 62 63
table, what are P(A and E) and P(CJE)?
TOTAL
27
38
60
125
(a) 12/25; 28/125
12/63; 28/60
12/125; 28/63
(d) 12/125; 28/60
(e) 12/63; 28/63
2. For the tree diagram pictured, what is P(BIX)?
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4
(
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x
V
z
(a) 1/4
5/17
(c)2/5
(d)1/3
(e)4/5
3. Given that P(A)
(a)P(A and B)
=
0.6, P(B)
=
0.3, and P(BjA)
=
0.5, find the following probabilities:
(
(b)P(A or B)
(c) Are events A and B independent?
4. Given that P(A) = 0.25 and P(B) = 0.35, find P(A or B) if
(a) A and B are mutually exclusive
(b) A and B are independent
5. A player serving in tennis has two chances to get a serve into play. If the first serve
goes out of bounds, the player serves again. If the second serve is also out, the
player loses the point. Here are probabilities based on the last four years of the
Wimbledon Championship:
p(lst serve is in) = 0.59
P(win point
serve in) = 0.73
P(2 serve in 1 serve out) = 0.86
P(win point I 1 serve out and 2 serve in) = 0.59
(a) Make a tree diagram for the results of the two serves and the outcome (win or
lose) of the point.
(b) What is the probability that the serving player wins the point? Show your work.
(Q,
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6. According to the Arizona chapter of the American Lung Association, 7.0% of the
population has lung disease. Of those having lung disease, 90.0% are smoker; of
those not having lung disease, 25% are smokers. Determine the probability that a
randomly selected smoker has lung disease.
‘%
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7. According to the Heart Association, 8% have heart disease. The probability that one
tests positive when you have heart disease is 96%. It is also known that 7% will test
positive when they don’t actually have heart disease. What is the probability that a
person actually has heart disease if they test positive?
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p_J
N
I
8 Here are the counts (in thousands) of earned degrees in the United States in a recent
year classified by level and by the sex of the deqree recipient:
BACHELOR
j PROFESSIONAL DOCTORATE TOTAL I
MASTERS
FEMALE
616
j
194
30
I
16
856
529
171
44
[ MALE
26
770
1145
IIOTAL
365
74
42
1626
]
Use proper notation to answer the following questions:
(a)If you choose a degree recipient at random, what is the probability that the person
you choose is a woman?
(b)What is the probability that a randomly chosen degree recipient is a man?
-
si
—
(c) What is the probability that you choose a woman, given that the person chosen
received a professional degree?
(d)What is the probability that the person chosen received a bachelor’s degree, given
that he is a man?
(e)Are the events “choose a woman” and “choose a professional degree recipient”
independent?
0
(f) Find the probability of choosing a male bachelor’s degree recipient from the table of
counts above.
(g)Confirm your answer to (f) by using the multiplication rule to find the probability of
choosing a male bachelor’s degree recipient.
0
9. Suppose that, in a certain part of the world, in any 50-year period the probability of a
major plague is 0.39, the probability of a major famine is 0.52, and the probability of
both a plague and a famine is 0.15. What is the probability of a famine given that
thereisapiague?
vccnp’i
(a)0.240
(b)0.288
0.370
ICO.385
(e) 0.760
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(c)
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10. Given the probabilities P(A) = 0.4 and P(A U B) = 0.6, what is the probability of P(B)
if A and B are mutually exciusive? If A and B are independent?
a 0.2,0.4
c.S)e vcck—9Ct
0.2, 0.33
ebb.
4. ?
c 0.33, 0.2
qc%Nc.
z.
(d) 0.6, 0.33
(e) 0.6, 0.4
%
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ii. In an effort to find the source of an outbreak of food poisoning at a conference, a
team of medical detectives carried out a study. They examined all 50 peopie who had
food poisoning and a random sampie of 200 peopie attending the conference who
didn’t get food poisoning. The detectives found that 40% of the peopie with food
poisoning went to a cocktail party on the second night of the conference, while only
10% of the people in the random sample attended the same party. Which of the
foiiowing statements is appropriate for describing the 40% of peopie who went to the
party? (Let F a got food poisoning and A a attended party).
(a) P(F I A) = 0.40
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(b) P(A I F = 0.40
(c) P(F I A) = 0.40
(d)P(A’ I F) = 0.40
(è))None of these
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12. A travel agent books the passages on three different tours, with half her customers
choosing tour Ti, one-third choosing 12, and the rest choosing T3. The agent has
noted that three-quarters of those who take tour Ti return to book passage again,
two-thirds of those who take tour 12 return, and one-half of those that take tour T3
return. If a customer does return, what is the probability that the person first went
ontourT2?
?
(a) 1/3
,1%
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(b)2/3
..R. a13
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(c)2/9
V
Ji6/49
TA ‘3
13
a
(J 49/72
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