Probability help needed.

Hello all.

I am a little confused by this question. I think it's conditional probability but not sure. Just cannot get my head around it

The question is

"A laboratory blood test is 80% effective in detecting a certain disease when it is present in the person tested. However, the test also gives a 'false positive' result in 5% of those tested who do not have the disease. Suppose that 0.4% of the population actually have the disease. What is the probability that a person with a positive test result actually has the disease?"

Enter your answer in the box below, to 3 decimal places.

I put 0.004 but I certain this is wrong.

Any help would be appreciated as well as an explanation if they have time.

Thanks again.

Draw a tree diagram with branches: Diseased and not diseased and from each of these branches draw another two for positive result and negative result - then think of conditional probability.

it is conditional probability.

i used this tree diagram:

since it is P ( positive | has disease )

you put any of A, B, C, D underneath ( added ) as the denominator, and one of them on top.

Hello all.

I am a little confused by this question. I think it's conditional probability but not sure. Just cannot get my head around it

The question is

"A laboratory blood test is 80% effective in detecting a certain disease when it is present in the person tested. However, the test also gives a 'false positive' result in 5% of those tested who do not have the disease. Suppose that 0.4% of the population actually have the disease. What is the probability that a person with a positive test result actually has the disease?"

Enter your answer in the box below, to 3 decimal places.

I put 0.004 but I certain this is wrong.

Any help would be appreciated as well as an explanation if they have time.

Thanks again.