statistics HW

[Skoally]

I am having issues trying to understand how to calculate some probability problems. I understand that I can not be given the answer - I would not want that anyway. I need to know how to get the answer so that I can do the rest of the questions like it.

 

the problem is as follows:

 

10 composite samples are used to run a composite test, and the probability that any one sample will test positive is 0.0400

 

what is the probability that the composite sample will test NEGATIVE?

 

What is the Probability that composite sample will test POSITIVE?

 

HOW DO I FIND THE ANSWER, in layman's terms please. I am a stats student right now.

[Mr Skeptic]

It doesn't look like you have enough info, not if the test can give an inconclusive result. It looks like you're given the answer to your second question?

 

But I haven't heard of a composite test. Does that have another name?

[Skoally]

It doesn't look like you have enough info, not if the test can give an inconclusive result. It looks like you're given the answer to your second question?

 

But I haven't heard of a composite test. Does that have another name?

 

the problem in its entirety is as follows:

It can be very expensive to do tests on medical samples, such as blood tests. One method of reducing the expense of such tests is to take the individual samples, take half of each, combine the half samples, and test the composite sample. If the composite sample tests negative for some condition, then all the original samples would have tested negative, and only the one test was needed, saving much money. However, if the composite sample tests positive, then there is no way of knowing which of the original samples would have tested negative and which positive. In that case, all the remaining have to be tested individually, and the test on the composite sample was an extra test, resulting in extra money being spent.

 

On your comment to having the answer to the second question, 10 samples for composite tests, and the probability that any one sample would test positive is .0400. That would be .04¹⁰ = 1.0486x10^-14 ?

Thank you for any guidance you can provide me with!

[Mr Skeptic]

I see. So the probability of one sample testing positive is .04, but 10 samples are tested simultaneously, with the test returning a positive if at least one sample is positive and negative if all samples are negative.

 

The negative is the easiest case to find, it is the probability of every sample testing negative (with probability 1 - .04 = .96 each).

The positive you can either calculate by summing the probabilities of 1, 2, 3, ..., 10 samples testing positive, but there is a much much easier way. Since the test will return positive or negative, the chance of the positive result is easy enough to find once you know the chance of the negative result.