A workshop's output comes from two machines: machine P makes 60% of the items and machine Q the other 40%. Of machine P's items 2% are defective, and of machine Q's items 5% are defective. An item picked at random from the day's output turns out to be defective. What is the probability that it was made by machine Q?

Take 1000 items. Machine P makes 600 of them and 2% of those are duds — 12 defective items. Machine Q makes 400 and 5% of those are duds — 20 defective items. Once a defective item is in hand, only those 32 matter, and 20 came from Q: 20/32 = 5/8. Trap 3/8 = 12/32 is the same calculation done for machine P; note 5/8 + 3/8 = 1. Trap 2/5 quotes machine Q's share of the OUTPUT and ignores the fact that a defective item has already been found. Trap 1/20 = 5% is Q's defect rate, which answers the reverse question 'given that an item is from Q, is it defective'.