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Oct 12 2010 03:40pm
Looking for a detailed explanation to these questions:

Two pumps connected in parallel fail independently of one another on any given day. The probability that only the older pump will fail is .1. Probability new one will fail is .05. What is the probability that the pump will faill on any given day?

- I assumed .1 x .05, which results in .005 but answer in book is .0059? What the heck?


Let A be asian project that's successful and B be european project that's successful. Suppose A and B are independent and P(A) is .4 and suppose P(B) is .7.
a. What is the probability at least one of the two projects is successful? (Answer is .82)
b. Given at least one project is successful, what is the probability that only the asian project is successful? (Answer is .146)



I'd greatly some help and may even be willing to donate ;)

Thanks!
- Tom

This post was edited by Call Me Traitor on Oct 12 2010 03:41pm
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Oct 12 2010 04:34pm
The probability that only the older pump will fail is .1. Probability new one will fail is .05.

Key word bolded. This translates into:

P(new one fails) = 0.05 = P(B )
P(old one fails AND new one does not fail) = 0.1 = P(A and not B )

Want to try it from there?

Other problem...

P(A) = 0.4
P(B ) = 0.7

a )

P(A or B ) = P(A) + P(B ) - P(A and B )

A and B are independent events, so we have
P(A and B ) = P(A)P(B ) = 0.4 * 0.7 = 0.28

P(A or B ) = 0.4 + 0.7 - 0.28 = 0.82

b )

Given "A or B". We want the probability that only A succeeds:

P(A and not B | A or B ) = P((A and not B ) and (A or B ))/P(A or B ) = P(A and not B )/P(A or B ) (note that "A or B" is a subset of "A and not B", so it doesn't affect the upper probability)
= P(A)P(not B )/P(A or B ) by independence
= P(A)(1 - P(B ))/P(A or B ) since P(not B ) = 1 - P(B )
= (0.4*(1 - 0.7))/0.82 = (.4*.3)/.82 = 0.146

This post was edited by GoodFun on Oct 12 2010 04:35pm
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