What Is the Probability That Exactly 12 of Them Will Remain Clean?

Question by Shawna: what is the probability that exactly 12 of them will remain clean?
A recent study showed that 45% of the patients that entered a drug rehabilitation center remained clean of drugs. out of a random sample of 30 patients, what is the probability that exactly 12 of them will remain clean?

Best answer:

Answer by Jay
P(X = 12) = (30 choose 12)(0.45)^12(0.55)^18

You have to multiply this all together. The 0.45^12 is the amount that you need that will be clean, exactly 12, at the given percent.

The 0.55^18 is the remaining members that will not be clean.
30 choose 12 is 30C12. This is your total sample, and the amount you choose.

Best of luck! 😀

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