A manufacturing facility utilizes two assembly lines, A and B. 60% of the factor

Question

A manufacturing facility utilizes two assembly lines, A and B. 60% of the factory's output passes through assembly line A and 40% passes through assembly line B. 15% of the output from assembly line A is defective and 10% of the output from assembly line B is defective. If an item chosen at random is found to be defective, find the probability that it passed through 2. (a) (b) assembly line A assembly line B 15,5 For married couples, the probability that the wife lives beyond the age of 70 is .60 while the probability that the husband lives beyond the age of 70 is .45. For a given married couple, assuming independence, find the probability of each of the following: 3. (a) Both live beyond the age of 70 (b) The husband lives beyond the age of 70, but the wife does not. (c) The wife lives beyond the age of 70, but the husband does not. (d) At least one of the two lives beyond the 70. (e) Neither one lives beyond the age of 70 120

Explanation / Answer

2.

Probability of defect in assembly A: 60%*15% = 9%

Probability of defect in assembly B: 40%*10% = 4%

Total probability of defect in the manufacturing facility = 9%+4% = 13%

a) given that it is defective, probability that it passed through assembly A = 9%/13% = 0.6923 = 69.23%

b) given that it is defective, probability that it passed through assembly B = 4%/13% = 0.3077 = 30.77%

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