Question

suppose that a computer chip company has just shipped 10,000 computer chips to a computer company. unfortunately, 10 of the chips are defective. (a) compute the probability that two randomly selected chips are defective using conditional probability. (b) the probability that the first randomly selected chip is defective is \\( \frac { 10 } { 10,000 } = 0.001 = 0.1 \\% \\). compute the probability that two randomly selected chips are defective under the assumption of independent events. (a) the probability is (round to eight decimal places as needed.)

Explanation:

Step1: Calculate the probability of the first chip being defective

The probability that the first chip is defective is \(P(A)=\frac{10}{10000}\)

Step2: Calculate the probability of the second chip being defective given the first is defective

After one defective chip is taken out, there are \(9\) defective chips left and \(9999\) chips in total. So \(P(B|A)=\frac{9}{9999}\)

Step3: Use the formula for conditional probability \(P(A\cap B)=P(A)\times P(B|A)\)

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Answer:

\(0.00000090\)