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p64_exercises-2_8

# p64_exercises-2_8 - 64 CHAPTER 2 PROBABILITY degraded by...

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Unformatted text preview: 64 CHAPTER 2 PROBABILITY degraded by skewed alignments, 5% of the read operations are degraded by off-center 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 off-center 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 page-view 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 red-hair 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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