SOLUTION: I have two probability questions that really through me a loop. Can someone answer the questions and show there work? I appreciate any help. Thanks a) The ventilation system a

Question 14603: I have two probability questions that really through me a loop. Can someone answer the questions and show there work? I appreciate any help.
Thanks
a) The ventilation system at a power station only functions properly if both machines A and B are working. The probabilities of failure for these machines are 0.07 and 0.03 based on simulation studies. If the machines operate independently, what is the probability that the ventilation system breaks down?
b) An alternative system is based on machones C and D, which both have probability of 0.22 of failing and again operate independently. The ventilation system will function properly so long as either (or both) of machines C AND D is working, what is the probability that the system fails?
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
these are both straightforward probability questions. Solutions are:

1.
P(A works and B works) = 0.93*0.97 = 0.9021
P(A works and B not works) = 0.93*0.03 = 0.0279
P(A not works and B works) = 0.07*0.97 = 0.0679
P(A not works and B not works) = 0.07*0.03 = 0.0021
The system fails when just one machine (or both) fails, so
P(ventilation sysyem breaks down) = last 3 possibilities added together

OR it is "everything less first one, ie
P(system fails) = 1 - P(both work)
P(system fails) = 1 - 0.9021
P(system fails) = 0.0979

2.
P(C works and D works) = 0.78*0.78
P(C works and D not works) = 0.78*0.22
P(C not works and D works) = 0.22*0.78
P(C not works and D not works) = 0.22*0.22 = 0.0484

The system fails when both fail, so this is 0.0484

jon.

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