(ii) A factory has two machines. Past records show that the first machine produces 40% of output and the second machine produces 60% of output. Further 4% and 2% of the products produced by the first machine and the second machine were defectives. If a defective item is drawn at random, what is the probability that the defective item was produced by the first machine or second machine?

Question

(ii)	A factory has two machines. Past records show that the first machine produces 40% of output and the second machine produces 60% of output. Further 4% and 2%  of  the products produced by the first machine and the second machine were defectives. If a defective item is drawn at random, what is the probability that the defective item was produced by the first machine or second machine?

Damon · Answer

say we make 1000 total 400 from #1, 16 defective 600 from #2, 12 defective Tat is a total of 28 defective 16/28 = .57 from #1 12/28 = .43 from #2