Q:An electronic fuse is pro-duced by five production companies in a man-ufacturing operation. The fuses are costly, are
quite reliable, and are shipped to suppliers in
100-unit lots. Because testing is destructive,
most buyers of the fuses test only a small num-
ber of fuses before deciding to accept or reject
lots of incoming fuses.
All five production lines produce fuses at the
same rate and normally produce only 2% de-
fective fuses, which are dispersed randomly in
the output. Unfortunately, production line 1
suffered mechanical difficulty and produces 5%
defectives during the month of March. This
situation became known to the manufacturer
after the fuses had been shipped. A customer
received a lot produced in March and tested
three fuses. One failed. What is the probabil-
ity that the lot was produced by line 1? What
is the probability that the lot came from one
of the other four lines?
A:Clearly P (B) = 0.2
Then
P (A|B) = 3(0.05)(0.95)^2 = 0.135375.
Sorry for the weird formatting, I copy and pasted this question.
I don't see how they got this part...
P (A|B) = 3(0.05)(0.95)^2 = 0.135375.
The section this question is asked in goes over total probability and Baye's rule, but I can't seem to get that result ussing those techniques.
I just need help with this step, everything else should follow.