Intro to Probability

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Widgets are produced at a certain factory by each of three machines A, B and C. These machines produce 1000, 600 and 400 widgets per day, respectively. The probability that a given widget is defective is 4% for one produced by Machine A, 3% if produced by Machine B, and 2% if produced by Machine C. Suppose that the Widget Inspector selects a widget at random from the factory's widget inventory.
(a) What is the probability that the widget is defective?
(b) If the widget is defective, what is the chance that it came from Machine A?
========================================
Answer a) is it 4+ 3+2 =9%
b) A=widget is defective
B=came from machine A
P(A& B)= P(A)P(B)
= .09* (1000/2000)= .045
= 4.5 %

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