Download Chapter 4: Probability

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Chapter 4 Practice Test Probability
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True-False Questions
1.____ If A and B are any two events of a sample space S, then the addition rule is:
P( A or B)  P( A)  P( B)  P( A and B) .
2. ____If A and B are any two independent events of a sample space S, then P(A and B) = P(A)  P(BA).
3. ____If two events are mutually exclusive, they are also independent.
4. ____If the sets of sample points belonging to two different events do not intersect, the events are mutually
exclusive or dependent.
5. ____If P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.18, then A and B are independent events.
6. ____If P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0.15, then P(B | A) = 0.45
Multiple-Choice Questions
7. ____Suppose A and B are independent events of a sample space S with P(A) = 0.30 and P(B) = 0.50, then P(A
and B) is
A.
0.80
B.
0.60
C.
0.20
D.
0.15
8. ____If P(A) = 0.80, P(B) =0.70 and P(A or B) =0.90, then P(A and B) is:
A.
0.10
B.
0.14
C.
0.60
D.
0.72
9. ____If P(A) = 0.45, P(B) = 0.35 and P(A and B) =0.25, then P(A | B) is:
A.
1.4
B.
1.8
C.
0.714 D.
0.556
10. ____If P(A) = 0.60, P(B) = 0.63, and P(A and B) = 0.73, then P(A or B) is:
A.
1.23
B.
0.50
C.
0.13
D.
0.10
11. ____Two events A and B are said to be independent if:
A.
P(A and B) = P(A) . P(B)
B.
P(A and B) = P(A) + P(B)
C
P(A | B) = P(B)
D.
P(B | A) = P(A)
12. ____Which of the following statements is always correct?
A.
P(A and B) = P(A) . P(B)
B.
P(A or B) = P(A) + P(B)
C.
P(A or B) = P(A) + P(B) + P(A and B) D.
P(A) = 1 - P ( A )
Short-Answer Questions
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Three identical slips of paper with the numbers 1, 2, and 3 (one number on each slip) are placed in a box.
One slip is randomly selected, and then, without replacement, a second slip is selected. Find the
probability that the sum of the two numbers is even.
Events A and B are mutually exclusive events defined on a common sample space. If P( A)  0.4 and
P( A or B)  0.9 , find P(B).
Events A and B are defined on a common sample space. If P(A) = 0.7, P(B) = 0.6, and A and B are
independent events, find P(A or B).
Events A and B are defined on a common sample space. If P(A) = 0.20, P(B) = 0.40, and
P(A or B) = 0.56, find P(A and B)
A box contains five red, three blue, and two white poker chips. Two are selected without replacement.
Find the probability that both are the same color.
Applied and Computational Questions
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Five cards are randomly selected from a standard deck of 52 cards. Find the probability that all five cards
are red if they are selected:
(a) without replacement
(b) with replacement
Events A, B, and C are events of a sample space S with A and C mutually exclusive, B and C mutually
exclusive, P(A) = 0.32, P(B) = 0.11, P(A and B) = 0.08, and P(C) = 0.42. Find each of the following
probabilities: (a) P(A or B) (b) P(A or C) (c) P(B or C) (d) P( A ) (e) P(C ) (f) P(A and C)
Five hundred people are classified based on their smoking habits and whether or not they have prominent
wrinkles. The results are shown below:
Prominent Wrinkles Wrinkles Not Prominent
Heavy smoker
120
60
Light or nonsmoker
75
245
One individual is randomly selected from that group of 500 people.
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CHAPTER FOUR
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a. Given that the individual is a heavy smoker, what is the probability that he/she does not have
prominent wrinkles?
b. What is the probability that the selected individual is a heavy smoker or has prominent wrinkles?
A box contains 12 red marbles and 8 blue marbles. Three marbles are randomly selected, one at a time.
Find the probability that all three are blue if they are selected:
a. with replacement
b. without replacement
An experiment consists of selecting a marble from box one and placing it in box two, and then a marble is
selected from box two and its color is noted. Box one contains two red, three blue, and five white
marbles, and box two contains six red, two blue, and two white marbles. Find the probability that:
a. the first and second selected marbles were both red.
b. the marble selected from box two was red
A medical clinic in Chicago classifies the patients’ files by gender and by type of diabetes (A or B). The
number of patients in each classification is shown below.
Type of Diabetes
Gender
A
B
Male (M)
50
40
Female (F)
70
40
If one file is selected at random, find the probability that the selected individual is:
a. female.
(b) Type B.
(c) Type A male
A hospital classifies some of the patients’ files by gender and by type of care received (Intensive Care
Unit (ICU) and Surgical Unit). The number of patients in each classification is presented below:
Type of Care
Gender
ICU
Surgical Unit
Male (M)
25
39
Female (F)
21
15
One of these patients is randomly selected.
a. Are the events “being a female” and “being in the ICU” mutually exclusive?
b. Are the events “being in the ICU” and “being in the surgical unit” mutually exclusive?
c. Find P(ICU or Female).
d. Find P(Surgical unit or Male).
e. Find P(ICU and Male)
Suppose that P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.18.
a. What is P(A|B)?
b. What is P(B|A)?
c. Are A and B independent? Justify your answer in three different ways.
A box contains 50 parts, of which 6 are defective and 44 are nondefective. If two parts are selected
without replacement, find the following probabilities:
a. P(both are defective)
b. P(exactly one is defective)
c. P(neither is defective)
P(A) = 0.3, P(B) = 0.4, and events A and B are mutually exclusive.
a. Find P(A and B).
b. Find P(A or B).
c. Find P(A or B).
d. Find P(A|B).
e. Find P(A| B )
f. Are events A and B independent? Explain.