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Probability and Statistics

Probability over years

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[quote][i]Originally posted by princemuggin[/i]
[br]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!
[/quote]

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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.