sam2304 wrote:A shipment consists of 1,800 parts, some of which are defective. If a part is chosen from the shipment at random, the probability of it being defective is 1/9 the probability that it is not defective. How many of the parts in the shipment are defective?
(A) 90
(B) 120
(C) 180
(D) 200
(E) 900
The probability that the part is defective is 1/9 the probability that it is not defective.
To determine the ratio of defective parts to non-defective parts, plug in.
If there are 9 non-defective parts, then the number of defective parts = (1/9)9 = 1.
Thus, of every 10 parts, the fraction that are defective = 1/(9+1) = 1/10.
Total number of defective parts = (1/10)1800 = 180.
The correct answer is
C.
We also could plug in the answer choices, which represent the number of defective parts.
Answer choice C: 180
P(defective) = 180/1800 = 1/10, implying that P(non-defective) = 1 - 1/10 = 9/10.
P(defective)/P(non-defective) = (1/10)/(9/10) = 1/9.
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