Unformatted text preview: 64 CHAPTER 2 PROBABILITY degraded by skewed alignments, 5% of the read operations are
degraded by offcenter alignments, and the remaining read op
erations are properly aligned. The probability of a read error is
0.01 from a skewed alignment, 0.02 from an offcenter align
ment, and 0.001 from a proper alignment. (a) What is the probability of a read error? (b) If a read error occurs, what is the probability that it is due to a skewed alignment? 2—161. The following circuit operates if and only if there is
a path of functional devices from left to right. Assume that de
vices fail independently and that the probability of failure of
each device is as shown. What is the probability that the
circuit does not operate? 2—162. A company that tracks the use of its web site deter
mined that the more pages a visitor views, the more likely the
visitor is to provide contact information. Use the following
tables to answer the questions: Number of
pages viewed: 1 2 3 Percentage of
visitors: 40 30 20 10 Percentage of visitors
in each pageview
category that provide
contact information: 10 4 or more 10 20 40 (a) What is the probability that a visitor to the web site
provides contact information? (b) If a visitor provides contact information, what is the
probability that the visitor viewed four or more pages? 2—163. An article in Genome Research “An Assessment of
Gene Prediction Accuracy in Large DNA Sequences,"
(2000, Vol. 10, pp. 1631—1642), considered the accuracy of
commercial software to predict nucleotides in gene se
quences. The following table shows the number of se
quences for which the programs produced predictions and
the number of nucleotides correctly predicted (computed
globally from the total number of prediction successes and
failures on all sequences). Number of sequences Proportion
GenScan . 177 0.93
Blastx default 175 0.91
Blastx topcomboN 174 0.97
Blastx 2 stages 175 0.90
GeneWise 177 0.98
Procrustes 177 0.93 Assume the prediction successes and failures are independent between the programs. (a) What is the probability that all programs predict a nu
cleotide correctly? (b) What is the probability that all programs predict a nu
cleotide incorrectly? (c) What is the probability that at least one Blastx program
predicts a nucleotide correctly? 2—164. A batch contains 36 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Six cells are . selected at random, without replacement, to be checked for replication. (a) What is the probability that all six cells of the selected
cells are able to replicate? (b) What is the probability that at least one of the selected
cells is not capable of replication? 2—165. A computer system uses passwords that are exactly seven characters and each character is one of the 26 letters (a—z) or 10 integers (0—9). Uppercase letters are not used. (a) How many passwords are possible? (b) If a password consists of exactly six letters and one num
ber, how many passwords are possible? (c) If a password consists of ﬁve letters followed by two num
bers, how many passwords are possible? 2—166. Natural red hair consists of two genes. People with
red hair have two dominant genes, two regressive genes, or
one dominant and one regressive gene. A group of 1000 people
was categorized as follows: Gene 2
Gene 1 Dominant Regressive Other
Dominant 5 25 30
Regressive 7 63 35
Other 20 15 800 Let A denote the event that a person has a dominant redhair
gene and let B denote the event that a person has a regressive
red hair gene. If a person is selected at random from this
group, compute the following. (a) P(A) (b) P(A n B) (c) P(A U B) (d) P(A’ n B) (e) P(AI B) (f) Probability that the selected person has red hair ...
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 Spring '08
 Wherly
 Statistics

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