Question 1: The following system operates if and only if there is a path offunct

Question

Question 1:

The following system operates if and only if there is a path offunctional components from left to right. In the system each of thethree components works independently of the others. The probabilitythat component B works is 0.95. The probability that component Bworks is also 0.95. The probability that system does not work is0.050475. Find the probability that component A work?

Look at this link to see how the system work (series &parallel):

http://img242.imageshack.us/img242/1364/picture7yd.png

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Question2:

Let C denote the event that a randomly selected person is acarrier of the disease.

Let P denote the event that the blood test is positive.

Suppose it is known that 1% of the population are carries ofparticular disease. A blood test has 97% chance of giving apositive test result correctly identifying carriers of the disease,but also has a 6% chance of giving a positive test result falselyindicating that a healthy person (i.e. non-carrier) has thedisease.

Thus,

P(C) = 0.01, P(P|c) = 0.97, and P(P|C’) = 0.06

a)     What is the probability that a personwill have a positive blood test?

b)    If your blood test is positive, what is thechance that you are a carrier of the disease?

c)     If your blood test is negative, what isthe chance that you are not a carrier of the disease?

Explanation / Answer

Since they're independent, you can find out the probability ofthe intersect by multiplying... Example: P(A & C) = P(A)P(C)... So, for the system to work, you need (A & C) or (B &C)... P(A)P(C) + P(B)P(C) = 1 - 0.050475 0.95[P(A) + 0.95] = 1 - 0.050475
P(A) = 0.0495

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