Question

Please give explanation with details: Three factories A, B, and C produce the same product. The factory A produces twice as many as B produces; while the factories B and C produce in the same quantity. It is known that 2% of the products of A as well as C are defective. Whereas 4% of the products of B are defective. All the products of the three factories are stocked together. If a product is selected at random from the stock, what is the probability that the product is defective?

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a produces say 2x

b and c produce x

2% of A, and C are defective. 4% of b is defective. So, .02*2x+.02*x+.04*x = .1x is defective

all products are stocked together.

P(randomly selected product from the stock is defective) = total defective products/total products = (.1x)/(2x+x+x) = 1/40 = .025 or 2.5%

So, answer is 2.5%

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