Question 659042: In a scientific study there are 14 guinea pigs, 9 of which are pregnant. If 3 are selected at random without replacement, find the probability that none are pregnant. Enter your answer as a fraction or as a number rounded to three decimal places. Correct answer: 5/182
I have the answer, but cannot figure out to get that fraction - Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 9 out of 14 guinea pigs are pregnant for a probability of 9/14.
3 are selected at random without replacement.
what is the probability that none are pregnant.
probability of a guinea pig being pregnant is 9/14.
probability of a guinea pig not being pregnant is 5/14.
the probability of the first guinea pig not being pregnant is 5/14.
the probability of the second guinea pig not being pregnant is 4/13.
the probability of the third guinea pig not being pregnant is 3/12.
the probability of all 3 not being pregnant is 5/14 * 4/13 * 3/12
this can be simplified to 5/14 * 4/13 * 1/4 which can be further simplified to 5/14 * 1/13 which is equal to 5/(14*13) which is equal to 5/182.
the alternate way of looking at is finding the probability by finding the number of ways you can get all non-pregnant women and dividing that by the number of ways you can get any women.
the formula for the number of ways to get 3 non-pregnant women out of a pool of 5 non-pregnant women is C(5,3) which is equal to 10.
the formula for the number of ways to get 3 women out of a pool of 14 women is C(14,3) which is equal to 364.
the probability is 10 / 364 which simplifies to 5/182.
pick the method you feel most comfortable with and go with that.
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