Two assembly lines I and II have the same rate of defectives in their production of voltage regulators. Six regulators are sampled from each line and tested. Among the total of twelve tested regulators, four are defective. Find the probability that exactly two of the defective regulators came from line I. (Round your answer to four decimal places.)

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Mathematics

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12 December, 14:54

Two assembly lines I and II have the same rate of defectives in their production of voltage regulators. Six regulators are sampled from each line and tested. Among the total of twelve tested regulators, four are defective. Find the probability that exactly two of the defective regulators came from line I. (Round your answer to four decimal places.)

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Heather Mooney · Answer 1

0.4546

Step-by-step explanation:

nCr = n! / (n-r) ! r!

Number of ways of selecting the four defective voltage regulators from 12 = 12C4 = 12! / (12-4) !4! = 12!/8!4! = (12 * 11*10*9) / (4*3*2*1)

12C4 = 495 ways

Number of ways of selecting 2 defectives from line 1 = 6C2 * 6C2

6C2 = 6! / (6-2) !2! = 6!/4!2! = (6*5) / (2*1) = 15

6C2 * 6C2 = 15*15 = 225 ways

Probability = Number of possible outcomes / Number of total outcomes

Probability that exactly 2 of the defective regulators came from line 1 = 225/40.95 = 0.4546