Answer to Question #166475 in Statistics and Probability for phemelo mongae

Question

Two machines are producing the same item. The previous week, Machine A produced 40% of the total output, and Machine B the remainder. On average, 10% of the items produced by Machine A were defective, and 4% of the items produced by Machine B were defective. (a) What proportion of the previous week’s entire production was defective? (b) If an item selected at random from the combined output is found to be defective, what is the probability it came from Machine A? 

Answer 1

1. Let's find defective propotion of all production for each machine. Machine A: 0.4*0.1 = 0.04 (4%); Machine B: 0.6*0.04 = 0.024 (2.4%). So the entire defective proportion is 2.4 + 4 = 6.4%
2. As we found before, the defective proportion for machine A was 4% and the entire defective proportion was 6.4%. So the probability is 4 / 6.4 = 0.625 (62.5%)