# Trick question

This stumped me, but I should have known better. I ended up guessing because my P (A | B) wasn’t working out. FYI A company has two machines that produce widgets. An older machine produces 16% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine employs a superior production process such that it produces three times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is NOT defective? A) 0.06. B) 0.50. C) 0.76. D) 0.92. Your answer: B was incorrect. The correct answer was D) 0.92. The problem is just asking for the conditional probability of a defective widget given that it was produced by the new machine. Since the widget was produced by the new machine and not selected from the output randomly (if randomly selected, you would not know which machine produced the widget), we know there is an 8% chance it is defective. Hence, the probability it is not defective is the complement, 1 – 8% = 92%.

Just don’t let the word “given” fool you. Most of the time given is used when refering to a joint probability question but be careful