The probabilities that machines X, Y, Z will be performing well are . Find the probability that at most two of the machines will be operating.
P(at most two operating)
This is found in my math book. Can anyone explain why we need to use 1-P(all operating)? and I found out this 1-P(all operating) cannot be used when finding P(all machines not working)... Why?
Consider events A,B defined as: A = (at most 2 functioning) and B = (all 3 functioning). A and B are complements of each other. In other words, B means: not A. So P(A) + P(B) = 1.
Originally Posted by cloud5
P(all machines not working) is (1-1/3)(1-1/4)(1-1/5). Do you see why?
Edit: Originally I used X,Y in place of A,B not noticing that this choice of letters conflicted with the machine names.
I understand now. Thank you. :)
Originally Posted by undefined