There are seven distinct ways to draw pills without replacing: good, bad, good; good, good, good; bad, bad, bad; good, good, bad; good, bad, bad; and so on. That said, when it comes to individual pills, there are 720 different distinct ways to draw the pills without replacing the ones already drawn. The odds of drawing all three defective pills in a single round are 0.001388889. To get the different ways of drawing without replacing, you multiply 10 by 9 by 8. For the odds, you multiply 1/10 by 1/9 by ⅛, subtracting one from the number each time.
These odds are not in anyone’s favor, since at least two of the defective pills can slip through and not get tested randomly. In fact, it’s more probable that the three pills drawn and tested will be the good pills, and no defective pills are drawn.
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