0
$\begingroup$

A component has a probability of 0.05 to have a certain defect (a) and 0.01 to have another defect (b). The two defects are independent. I have to find the probability that the component has only one defect knowing that is defective.

I've done this:

     _      _    _   

p(D)=1-p(D)=1-p(a)*p(b)=1-0.95*0.99=1-0.9405=0.0595

I started calculating the probability to have only one defect and I'd use the conditional probability with D when I had the result:

p([a/(a^b)]U[b/(a^b)])=p[a/(a^b)]+p[b/(a^b)]-p[[a/(a^b)]^[b/(a^b)]
I don't know how to continue.

$\endgroup$
  • 1
    $\begingroup$ Please add the [self-study] tag & read its wiki. $\endgroup$ – gung - Reinstate Monica Jan 16 '16 at 11:39
  • 1
    $\begingroup$ 1. Please define your symbols. 2. Your algebra starts p(D) = 1-p(D) ... this doesn't make sense. $\endgroup$ – Glen_b Jan 16 '16 at 11:42
  • 1
    $\begingroup$ Please format this better... your "top bars" are showing up incorrectly. $\endgroup$ – user1566 Jan 16 '16 at 17:55
1
$\begingroup$

As a concrete example (you could/should use percentages when doing a problem like this in general), suppose there are 10,000 components:

  • We know 500 have defect 1

  • We know 100 have defect 2

  • Because the defects are independent, we have .05*.01*10000 = 5 components with both defects.

If you know the component is defective, it is one of the 600 total defective components.

Of these defective components, only 5 have both defects, so 595 have only one defect.

Thus, the probability of only one defect is 595/600 or about 99.17%

Suggestion: avoid using formulas blindly, and consider doing a step-by-step analysis, at least while you're still learning.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.