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)
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Chapter1: Combinatorial Analysis
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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.
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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