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Math Help - Finding probability (2 questions)

  1. #1
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    Finding probability (2 questions)

    1) For a typical citizen the probability of going to the dentist in a one year period is 0.3. Four randomly individuals are interviewed as part of a health care study. Calculate

    i) The probability that three OR more individuals have visited the dentist during the past year


    I have been trying to solve this question for quite sometime now, but I do not seem to find the correct method for solving it? could somebody please help



    2) 10% of a certain type of component are fault. Two components of this type are fitted to a machine, which will function provided at least one of this components is not faulty. Stating the assumptions you make, calculate the probability that the machine will function.

    Attempt to answer:

    The probability that both components are faulty is 0.1 x 0.1 = 0.01 and therefore the probability that at least one of these components is working is 1-0.01 = 0.99

    But then how do I find the probability the machine will work?

    I know the formula

    P ( M | A ) = P ( M n A) / P(A)

    but this doesnt seem to help for this question. How can I solve it?


    Thank you very much for any help
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  2. #2
    Kai
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    First question is binomial distribution

    Let X denotes the number of citizen going to a dentist

    X~B(n,p)

    where n=4 and p=0.3

    U have to find P(X\geq3)

    Edit: the pmf for binomial is give by P(X=x) = nCx * (p)^x *(q)^(n-x)
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  3. #3
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    Thank you for the help Kai. It was very useful.


    Does anybody know how to solve question number 2 as well? please


    thank you
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  4. #4
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    Quote Originally Posted by gva0324 View Post
    1)

    2) 10% of a certain type of component are fault. Two components of this type are fitted to a machine, which will function provided at least one of this components is not faulty. Stating the assumptions you make, calculate the probability that the machine will function.
    Let X be the r.v. that the component is not faulty.

    P(X \geq 1)={2 \choose 1}(\frac {90}{100})(\frac{10}{100}) +(\frac {90}{100})^2
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  5. #5
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    Hello gva0324
    Quote Originally Posted by gva0324 View Post
    2) 10% of a certain type of component are fault. Two components of this type are fitted to a machine, which will function provided at least one of this components is not faulty. Stating the assumptions you make, calculate the probability that the machine will function.

    Attempt to answer:

    The probability that both components are faulty is 0.1 x 0.1 = 0.01 and therefore the probability that at least one of these components is working is 1-0.01 = 0.99

    But then how do I find the probability the machine will work?

    I know the formula

    P ( M | A ) = P ( M n A) / P(A)

    but this doesnt seem to help for this question. How can I solve it?


    Thank you very much for any help
    I think you have done all you need to do! The machine will function provided at least one component is working, and the probability of this (as you have correctly worked out) is 0.99. Therefore this is the answer!

    The assumption you have made is that the number of components available is sufficiently large that the probability that the second one is faulty is still 0.1, even if the first one is known to be faulty.

    Grandad
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