Answer to Question #130155 in Statistics and Probability for asmi

Question

Suppose that the companies A, B, C produce Laptops. Company A produces twice as many as B ; while B and C produce the same number. It is known that 2% of A, 2% of B and 4% of C are defective. All the Laptops produced are put into one shop, and then one Laptop is selected randomly. (i) Determine the probability that the Laptop is defective. (ii) Suppose the Laptop chosen is defective, what is the probability that Laptop is produced by company B. 

Answer 1

Let`s suppose that Company A produces 2X laptops. Then B and C produces X laptops each. A, B and C produces 100% percent of laptops totally. $2X+X+X=100\% \Rightarrow X=25\%$. Thus, A produces 50% of laptops, B - 25%, C - 25%. From 50% of laptops of A 2% are defective. Thus, $50\%*2\%=1\%$ of all laptops are defective and made by A. In the same way, $25\%*2\%=0.5\%$ are defective and made by B and $25\%*4\%=1\%$ are defective and made by C. The total probability that a laptop is defective equals $1\%+0.5\%+1\%=2.5\%$. If we take a laptop and it is defective, the probability that it is made by B equals $0.5\%/2.5\%=0.2=20\%$ .