I have tried what I feel like is everything and I am still coming up short! Please help!

Question

The Centers for Disease Control (CDC) estimates that 0.6% of Americans have AIDS. The HIV-1 tests correctly diagnose the presence of HIV in 99% of the persons who have it and correctly diagnose its absence in 89.5% of the persons who don't.

Find the probability that a person whose result is positive is actually negative.

Answer 1

It's hard to draw a tree diagram on this page.....so the possibilities are:

 

Have it and positive test.....    .006*.99 = .00594

Have it and negative test....    .006*.01 = .0006

Don't have and positive........  .994*.105 = .10437

Don't have it and negative....   .994*.895 =.88963

 

So testing positive is case 1 and case 3 which makes up .00594+.10437 = .11031...approximately 11%.

 

But getting a false positive is .10437 or about 10%.

 

So given that we know that they tested positive, the probability you are actually free of the disease is .10437/.11031 which equals .9461517541 or 94.615%.

 

Hopwe this helped.