SOLUTION: A batch of pills consist of 9 good pills and 3 that are defective (contain the wrong amount of the drug). If 4 pills are randomly selected without replacement, what is the probabil

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Question 1183656: A batch of pills consist of 9 good pills and 3 that are defective (contain the wrong amount of the drug). If 4 pills are randomly selected without replacement, what is the probability that all 3 of the defective pills are selected?
Found 2 solutions by VFBundy, ikleyn:
Answer by VFBundy(438) About Me  (Show Source):
Answer by ikleyn(52874) About Me  (Show Source):
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A batch of pills consist of 9 good pills and 3 that are defective (contain the wrong amount of the drug).
If 4 pills are randomly selected without replacement, what is the probability
that all 3 of the defective pills are selected?
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We should calculate the number of the quadruples that contain 3 defective pills and 1 good pill.


Then we should relate this number to the number of all possible quadruples of 9+3 = 12 pills.


The numerator of the fraction is  C%5B3%5D%5E3%2AC%5B9%5D%5E1 = 1*9 = 9.


The denominator of the fraction is  C%5B12%5D%5E4 = %2812%2A11%2A10%2A9%29%2F%281%2A2%2A3%2A4%29 = 495.


The final probability under the problem's question is  9%2F495 = 1%2F55 = 0.01818 = 1.818%  (rounded).    ANSWER

Solved.