Question

A company uses two machines, A and B, to make boxes. Machine A makes 60 % of the boxes. 80 % of the boxes made by machine A pass inspection. 90 % of the boxes made by machine B pass inspection. A box is selected at random. (a) Find the probability that it passes inspection. (3) (b) The company would like the probability that a box passes inspection to be 0.87. Find the percentage of boxes that should be made by machine B to achieve this.

Answer 1

(a) P(box passes inspection) =

.6(.8) + .4(.9) = .48 + .36 = .84

(b) .8(1 - x) + .9x = .87

.8 - .8x + .9x = .87

.8 + .1x = .87

.1x = .07

x = .7 = 70%

Machine B--70% of boxes