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A particular component is used in assembling products. We obtain two thirds of these components from Supplier A and the rest from Supplier B. One percent of the components from Supplier A are defective, while two percent of Supplier B’s are defective.

  1. What is the probability that a randomly selected component is defective?
  2. Given that a randomly selected component is defective, what is the probability that it came from Supplier A?
  3. Let A be the event that a randomly selected component came from Supplier A and D be the event that a randomly selected part is defective. Are A and D independent? Explain?

For part $(1)$, my attempt at an answer is $\dfrac{2}{3}\dfrac{1}{100}+\dfrac{1}{3}\dfrac{2}{100} = \dfrac{4}{300} = .01\overline{33}$

This sounds right to me, because it makes sense that the chances are slightly higher than 1%, due to the fact that Supplier B is defective more often.

I do not know how to do $(2)$. Please help.

For $(3)$, I believe the answer is Yes because each event has its own probability of occurring, and $A$ can occur when $D$ does not, they both can occur, neither can occur, etc.

Thanks.

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For part 2 you should use Bayes' formula.

For part three, independence means that probability of one event doesn't depend on the other, i.e. P(D) is fixed wether A or not A. Is that so in this case?

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  • $\begingroup$ So just because the probability of $P(D)$ changes based on $P(A)$, they are dependent? I was looking at the fact that both can happen. Thanks for the answer. $\endgroup$
    – David
    Feb 20 '14 at 16:54
  • $\begingroup$ So for $(2)$, I got the answer of $.\overline{6666}%$ calculating it this way: $P(Coming from A) * P(defective from A)$. What do you think? $\endgroup$
    – David
    Feb 20 '14 at 17:08

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