Probability ??? ~~請數學高人幫幫手!!

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一條probability question:


(1) A factory specializes in producing a special kind of screw used in
building bridges. The diameter of the screws produced has to be within a
specified standard range. Screws are produced by three machines in the
factory. Machine A produces 25% of the total output. However, an
average of eight screws in every 1,000 produced by Machine A are found
to be not within the standard. Machine B produces 55% of the total
output with an average of five screws in every 1,000 being not within the
standard. The probability is 0.0008 that a randomly selected screw is not
within the standard and is produced by Machine C.


a) What is the probability that a randomly selected screw is not within
the standard?


b) If a randomly selected screw is not within the standard, what is the
probability that it is produced by Machine C?


c) If a randomly selected screw is within the standard, what is the
probability that it is produced by Machine A?


d) Construct a probability tree to display all the conditional probabilities
and the joint probabilities involved with respect to the above
situation. (You are not required to put down the numerical value of
the probabilities in the tree.)