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Geostatistics
Petroleum and Geosystems Engineering 337 (19065)
Spring 2008
Homework Assignment #2
Section 2.1
(Page 60)
3.
A section of an exam contains four TrueFalse questions. A completed exam
paper is selected at random, and the four answers are recorded.
a
List all 16 outcomes in the sample space.
Ans
According to the given, we can select either true or false 4
times for one completed answer.
TTTT, TTTF, TTFT, TFTT
FTTT, FFTT, FTFT, FTTF,
TFFT, TFTF, TTFF, TFFF,
FFFT, FFTF, FTFF, FFFF
b
Assuming the outcomes to be equally likely, find the probability that
all the answers are the same.
Ans
From the list of 16 outcomes, there are only 2 outcomes giving
the same answers (TTTT, FFFF). Hence, the probability is
2/16
or
1/8
c
Assuming the outcomes to be equally likely, find the probability that
exactly one of the four answers is “True”.
Ans
From the list of 16 outcomes, there are only 4 outcomes having
one “True” in the answer. Hence, the probability would be
4/16
or
1/4
d
Assuming the outcomes to be equally likely, find the probability that at
most one of the four answers is “True”.
Ans
This is an extension of part c; we know from part c that the
probability of exactly 1 “True” is 4/16. But the question asks
“at most” 1 “True” which means we need to include the case of
0 “True” which is the FFFF outcome, which makes the answer
to this question
5/16
.
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View Full Document5.
A box contains four bolts. Two of them, labeled #1 and #2 are 5 mm in
diameter, and two of them, labeled #3 and #4 are 7 mm in diameter. Bolts are
randomly selected until a 5 mm bolt is obtained.
The outcomes are the
sequences of bolts that can be selected. So one outcome is 1, and another is
342.
a
List all possible outcomes.
Ans
For all outcomes, we can randomly selected four of them until
we’ve got either 1 or 2 since both have 5 mm diameter. Hence,
there will be 10 outcomes in total as shown below.
1, 2, 31, 32, 341, 342, 41, 42, 431, 432.
b
Let A be the event that only one bolt is selected, list the outcomes in A.
Ans
A

( 1, 2)
c
Let B the event that three bolts are selected. List the outcomes in B.
Ans
B

(341, 342, 431, 432)
d
Let C be the event that bolt#2 is selected. List the outcomes in C.
Ans
C

(2, 32, 342, 42, 432)
e
Let D be the event that bolt#4 is
NOT
selected. List the outcomes in D.
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 Spring '08
 Jablonowski

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