Binomial Distribution Problem

I have been having issues figuring out this binomial distribution problem listed below. I know the answer is .1805, which I ended up getting wrong. I was curious on the steps to solve this question, I came up with the following list of variables to use when solving but I believe I am way off course.

p = .004 <---- 1\250
q = .996
n = 50
x = 2

[FONT=&quot]A test given to detect the HIV Aids virus in a person produces a false positive 1 out of every 250 times, which means a person who does not have the virus has test results they say they do. If 50 people are tested, what is the probability that 1 or 2 people tests positive even though they do not have the virus?

Any chance someone could tell me where I am going wrong or list the steps to solve?

Thanks,
Adam[/FONT]

AdamC said:

I have been having issues figuring out this binomial distribution problem listed below. I know the answer is .1805, which I ended up getting wrong. I was curious on the steps to solve this question, I came up with the following list of variables to use when solving but I believe I am way off course.

p = .004 <---- 1\250
q = .996
n = 50
x = 2

A test given to detect the HIV Aids virus in a person produces a false positive 1 out of every 250 times, which means a person who does not have the virus has test results they say they do. If 50 people are tested, what is the probability that 1 or 2 people tests positive even though they do not have the virus?

Any chance someone could tell me where I am going wrong or list the steps to solve?

Thanks,
Adam

Click to expand...

First, this is a terrible question. I'll tell you why, later.

\(\displaystyle P(1) = 50 \cdot \left( \dfrac{1}{250} \right)^{1} \cdot \left( \dfrac{249}{250} \right) ^{49} = 0.16500\)

You do p(2). Get the binomial coefficient right!

Here's the problem with the question. In order for this analysis to be correct as it stands, there must be NO test subject with HIV. If anyone has HIV, then we cannot get a false positive from that participant. If there is no test subject with HIV, why are we doing the screening?