A production line involves the use of three machines consecutively. The chance that the first machine will break down in any one week is 1/10. The chance of 1/20 for the second machine and 1/40 for the third machine. (i) Calculate the probability that all three machines are working consecutively. (ii) Calculate the probability that at least one of the machines will break down in a certain week. (iii) Calculate the probability that the first machine or the second machine will break down in a certain week
A production line involves the use of three machines consecutively. The chance that the first machine will break down in any one week is 1/10. The chance of 1/20 for the second machine and 1/40 for the third machine. (i) Calculate the probability that all three machines are working consecutively. (ii) Calculate the probability that at least one of the machines will break down in a certain week. (iii) Calculate the probability that the first machine or the second machine will break down in a certain week
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
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![A production line involves the use of three machines consecutively. The chance
that the first machine will break down in any one week is 1/10. The chance of
1/20 for the second machine and 1/40 for the third machine.
(i)
Calculate the probability that all three machines are working
consecutively.
(ii)
Calculate the probability that at least one of the machines will break
down in a certain week.
(iii)
Calculate the probability that the first machine or the second machine
will break down in a certain week
(iv)
Calculate the probability that the first machine breaks down if the third
machine breaks down.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0093f37-c9f3-4a67-912b-d15498cefa8d%2F638bd03a-fa7d-42dc-bd1e-6e24582aeb60%2Ff3g33id_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A production line involves the use of three machines consecutively. The chance
that the first machine will break down in any one week is 1/10. The chance of
1/20 for the second machine and 1/40 for the third machine.
(i)
Calculate the probability that all three machines are working
consecutively.
(ii)
Calculate the probability that at least one of the machines will break
down in a certain week.
(iii)
Calculate the probability that the first machine or the second machine
will break down in a certain week
(iv)
Calculate the probability that the first machine breaks down if the third
machine breaks down.
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