Thread: Random selection without replacement.

In a certain factory, machines I, II, III are all producing springs of the same length. Machines I, II, and III produce 1%, 4% and 2% defective springs, respectively. Of the total production of springs in the factory, Machine I produces 30%, Machine II products 25%, and Machine III produces 45%. If one spring is selected at random from the total springs produced in a given day, determine the probability that it is defective.

I know that this must involve the intersection of the percentages of defective springs given those produced by the machines, but I can't put it together. Will someone please help me get started? Thanks.

I think I might just produce 1000 springs and see how it goes.

I: 1000 * 0.30 = 300, then 300 * 0.01 = 3
II: 1000 * 0.25 = 250, then 250 * 0.04 = 10
III: 1000 * 0.45 = 450, then 450 * 0.02 = 9

In 1000 springs, we have 22 defectives. No what?

Aha! Thank you; the number of springs produced does seem to be the magic number I was missing. I'll try that and see what I can do. Thank you, again, for your help.