Question

A biotechnology company produced 189 doses of somatropin, including 11 which were defective. Quality control test 13 samples at random, and rejects the batch if any of the random samples are found defective. What is the probability that the batch gets rejected?

Answer 1

so you want to compute the probability that none are rejected, and subtract that answer from one

Answer 2

I've tried multiple times but I keep getting the wrong answer!

Answer 3

lets compute the probability that none are defective

Answer 4

you sample 13, and you want to make sure none of them are defective
there are 11 defective and 178 not defective

Answer 5

easiest way to compute this is
\[\frac{\binom{178}{13}}{\binom{189}{13}}\]

Answer 6

that is, the number of ways to choose 13 out of the non defective ones, divided by the total number of ways to choose the 13 out of all of them

Answer 7

you might have seen this written as
\[\frac{_{178}C_{13}}{_{189}C_{13}}\]

Answer 8

compute that number, subtract it from one

Answer 9

okay, one second!

Answer 10

http://www.wolframalpha.com/input/?i=%28178+choose+13%29%2F%28189+choose+13%29

Answer 11

subtract that number from one
that is the probability that none of the thirteen are defective

Answer 12

here is the final answer, about \(0.553\)
http://www.wolframalpha.com/input/?i=1-%28178+choose+13%29%2F%28189+choose+13%29

Answer 13

Got it, thank you!!!

Answer 14

yw