MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability
Problem
A factory has two machines, A and B. Machine A produces 8{,}000 items per day, while machine B produces 12{,}000 items per day. In one day, 240 items coming from machine A are found to be defective and 360 items coming from machine B are found to be defective.
(i) Treating these numbers as long-run frequencies, find:
(a) P(A), the probability that a randomly chosen item was produced by machine A.
(b) P(D), the probability that a randomly chosen item is defective.
(c) P(A∩D), the probability that an item is produced by machine A and is defective.
(ii) Using your answers from part (i), calculate P(A∣D), the probability that a defective item was produced by machine A.
(iii) Calculate P(D∣A), the probability that an item produced by machine A is defective.