Question 14603
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.