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Math Help - probability

  1. #1
    Member
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    probability

    Hi,
    I have issues understanding probability.
    I have this problem:

    A device for checking welds in pumps is designed to signal if the weld is defective. If the weld is actually defective, the probability the device will give a signal is .94.
    If the weld is actually not defective, the probability the device will give a signal is .05.
    It is known that 3% of welds on pumps are defective. A weld is selected at random and checked by the device.
    1- What is the probability the device will be correct?
    2- Suppose the device gives a signal for the checked weld. What is the probability the weld is actually not defective (false positive)?


    For the first question,
    I did this:
    P(device correct)=(.97)(.94)

    The second I dont know what to do.

    Please can someone help me ?
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  2. #2
    Grand Panjandrum
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    [quote=braddy;38768]Hi,
    I have issues understanding probability.
    I have this problem:

    A device for checking welds in pumps is designed to signal if the weld is defective. If the weld is actually defective, the probability the device will give a signal is .94.
    If the weld is actually not defective, the probability the device will give a signal is .05.
    It is known that 3% of welds on pumps are defective. A weld is selected at random and checked by the device.
    1- What is the probability the device will be correct?
    2- Suppose the device gives a signal for the checked weld. What is the probability the weld is actually not defective (false positive)?

    1- The device can be correct in two ways: the weld can be defective and the device says so, the welld could be OK and the device does not say its defective.

    pr(correct)=pr(defctv)pr(declared defctv when it is) + pr(not-defctv)pr(not declared defctv when it is not)

    ......=0.03*0.94 + 0.97*(1-0.05)=0.9497

    RonL

    (I will get back to 2 if nobody else does it - but I have to go now the dog is
    pestering to be taken for his walk)
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  3. #3
    Grand Panjandrum
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    [quote=braddy;38768]Hi,
    I have issues understanding probability.
    I have this problem:

    A device for checking welds in pumps is designed to signal if the weld is defective. If the weld is actually defective, the probability the device will give a signal is .94.
    If the weld is actually not defective, the probability the device will give a signal is .05.
    It is known that 3% of welds on pumps are defective. A weld is selected at random and checked by the device.
    1- What is the probability the device will be correct?
    2- Suppose the device gives a signal for the checked weld. What is the probability the weld is actually not defective (false positive)?

    2- If there are N welds tested, of these 0.03N are defective, and of these
    0.94(0.03N) give a positive signal.

    There are 0.97N non defectives and of these 0.05(0.97N) give a positive
    signal.

    So the probability that the weld is not defective given that the device gives
    a positive signal is the ratio of the number of non-defectives giving a positive
    signal to the total number of positive signals:

    0.05(0.97N)/[0.05(0.97N)+0.94(0.03N)]=0.0485/[0.0485+0.0282]=0.632

    (scarry Eh?)

    RonL
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  4. #4
    Member
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    very scary!
    Thanks captainBlack!
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