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Math Help - the probability that at least one of them will have a thyroid deficiency

  1. #1
    Yan
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    the probability that at least one of them will have a thyroid deficiency

    Medical records show that one out of 10 persons in a certain town has a thyroid deficiency. If 12 persons in this town are randomly chosen and tested, what is the probability that at least one of them will have a thyroid deficiency?
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  2. #2
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    Quote Originally Posted by Yan View Post
    Medical records show that one out of 10 persons in a certain town has a thyroid deficiency. If 12 persons in this town are randomly chosen and tested, what is the probability that at least one of them will have a thyroid deficiency?
    Tell us the probability that none of the twelve has the condition.
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    Let  P(A) be the probability of at least 1 person from 12 having the deficiency.

    Let  P(B) be the probability of nobody from 12 having the deficiency.

    We can conclude that  P(A) = 1 - P(B)

    Now we just need  P(B)

    Now. If you have 12 people, and each of them has a 0.1 chance of having the deficiency. Then you can say that 12 people have a 0.9 chance of NOT having the deficiency. So what's the probability that ALL of will NOT have the deficiency? Well we know that if two events have 2 probabilities of occuring, then the probability of both occuring is the product of their probabilities. This works the same, although instead of the product of 2 probabilities, we have the product of 12!.  P(B) = 0.9^{12} .

     P(B) = 1 - P(B)

     P(B) = 1 - 0.9^{12}
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