1. Of all failures of a certain type of computer hard drive, it is determined that in 20% of them only the sector containing the file allocation table is damaged, in 70% of them only nonessential sectors are damaged, and in 10% of the cases both the allocation sector and one or more nonessential sectors are damaged. A failed drive is selected at random and examined. a. What is the probability that the allocation sector is damaged? b. What is the probability that a nonessential sector is damaged? c. If the drive is found to have a damaged allocation sector, what is the probability that some nonessential sectors are damaged as well?

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1. Of all failures of a certain type of computer hard drive, it is determined that in 20% of them only the
sector containing the file allocation table is damaged, in 70% of them only nonessential sectors are
damaged, and in 10% of the cases both the allocation sector and one or more nonessential sectors are
damaged. A failed drive is selected at random and examined.
What is the probability that the allocation sector is damaged?
b. What is the probability that a nonessential sector is damaged?
c. If the drive is found to have a damaged allocation sector, what is the probability that some
nonessential sectors are damaged as well?
d. If the drive is found to have a damaged nonessential sector, what is the probability that the
allocation sector is damaged as well?
e. If the drive is found to have a damaged allocation sector, what is the probability that no
nonessential sectors are damaged?
f. If the drive is found to have a damaged nonessential sector, what is the probability that the
allocation sector is not damaged?
2. A system consists of four components connected as shown in the following diagram:
A
C
O
B
Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.10, 0.05,
0.10, and 0.20, respectively, what is the probability that the system functions?
Transcribed Image Text:1. Of all failures of a certain type of computer hard drive, it is determined that in 20% of them only the sector containing the file allocation table is damaged, in 70% of them only nonessential sectors are damaged, and in 10% of the cases both the allocation sector and one or more nonessential sectors are damaged. A failed drive is selected at random and examined. What is the probability that the allocation sector is damaged? b. What is the probability that a nonessential sector is damaged? c. If the drive is found to have a damaged allocation sector, what is the probability that some nonessential sectors are damaged as well? d. If the drive is found to have a damaged nonessential sector, what is the probability that the allocation sector is damaged as well? e. If the drive is found to have a damaged allocation sector, what is the probability that no nonessential sectors are damaged? f. If the drive is found to have a damaged nonessential sector, what is the probability that the allocation sector is not damaged? 2. A system consists of four components connected as shown in the following diagram: A C O B Assume A, B, C, and D function independently. If the probabilities that A, B, C, and D fail are 0.10, 0.05, 0.10, and 0.20, respectively, what is the probability that the system functions?
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