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 Probability over years

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T O P I C    R E V I E W
princemuggin Posted - 03/26/2012 : 15:43:51
I'm struggling with the following question. Essentially I keep second guessing myself! Here is the question:

A car plant purchases a new production line. The designer of the production line claims that there is a 5% probability that the machine breaks down in the first year. If it has not broken down during the first year there is a 10% probability that it breaks down in the second year. If it doesn’t break down during the first or second year there is a probability of 30% that it breaks down in the third year.

a) Calculate the probability that the production line won’t break down during the first two years.
b) Calculate the probability that the production line won’t break down during the first three years.
c) Suppose that the computer system undergoes a service and refit at the end of each year. The chances or breakdown in a particular year are now considered to be the same, 5% for each year. In this case, what is the probability that the system doesn’t break down during the first three years?

a) For this I have 95% in year 1 and then 94.7% in year 2. I find the second figure too high.
b) For this one I have 73.9%
c) Not sure.

However, I also came up with this answer:

a) 86% over the 2 years
b) 60% by year 3
c) 86% over the 3 years

Am I even going about this right?? Help much appreciated!
1   L A T E S T    R E P L I E S    (Newest First)
royhaas Posted - 03/26/2012 : 16:06:19
For a) I get 0.855. That should help. Think about conditional probabilities and independent events.

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