A machine produces tempered glass for mobile phones. The tempered glass produced is either grade A (good), grade B (minor defects) or grade C (unacceptable). The glass produced is put through an inspection machine that is able to detect any grade C glass and discard it. We may assume that the machine makes no mistakes in the detection process, meaning that given a piece of grade C glass, the probability of it being discarded is 1. At the same time, given a piece of grade A or B glass, the probability of it being discarded is 0. All the pieces of glass that are not discarded by the inspection machine will be packed and shipped to various wholesalers.

Suppose the machine produces grade A glass 90% of the time, grade B glass 2% of the time and grade C glass 8% of the time. Which of the following is the probability (computed to 3 significant figures), denoted by p, that a piece of glass that is not discarded by the inspection machine is grade A? MCQ

a) 0.978

b) 0.900

c) Not enough information for p to be computed.

d) 0.920