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A test to determine whether a certain antibody is present is 99.7% effective. This means that the test will accurately come back negative if the antibody is not present(in the test subject). The probability of a test coming back positive when the antibody is not present (a false positive) is 0.003.
Suppose the test is given to five randomly selected people who do not have the antibody.
(a) What is the probability that the test comes back negative for all five people?
(b) What is the probability that the test comes back positive for at least one of the five people?

Question

Help with stats?

A test to determine whether a certain antibody is present is 99.7% effective. This means that the test will accurately come back negative if the antibody is not present(in the test subject). The probability of a test coming back positive when the antibody is not present (a false positive) is 0.003. 
Suppose the test is given to five randomly selected people who do not have the antibody.
(a) What is the probability that the test comes back negative for all five people?
(b) What is the probability that the test comes back positive for at least one of the five people?

ganeshie8 · Answer

All 5 ppl do not have the antibody. So we expect the test to come back negative for all of them.

ganeshie8 · Answer

Remember, "test is positive" means "antibody is present"

 "test is negative" means "antibody is not present"

ganeshie8 · Answer

Now look at part a
`(a) What is the probability that the test comes back negative for all five people?`

ganeshie8 · Answer

We are given :
P("negative when the person has no antibody") = 0.997
P("positive when the person has no antibody") = 0.003

ganeshie8 · Answer

For part a, we want the test result to be "negative" for all 5 ppl

ganeshie8 · Answer

Can you guess what the probability must be ?

yanasidlinskiy · Answer

0.003?

yanasidlinskiy · Answer

*0.997

ganeshie8 · Answer

The 5 ppl we picked have no antibodies right ?

ganeshie8 · Answer

It is given in the problem :
`Suppose the test is given to five randomly selected people who do not have the antibody.`

yanasidlinskiy · Answer

I know. It's 0.997

ganeshie8 · Answer

Nope, we have 5 ppl remember

ganeshie8 · Answer

It should be 0.997* 0.997* 0.997* 0.997* 0.997

yanasidlinskiy · Answer

Okay, so I'd multiply that pretty much like 0.997^5 right?

ganeshie8 · Answer

Yes

yanasidlinskiy · Answer

Would I take the answer from part A and subtract that from 1?

yanasidlinskiy · Answer

or more like 1 - that answer from part A?
Or like 1-0.997 
Lol.

ganeshie8 · Answer

Briliant!

yanasidlinskiy · Answer

So... 1-0.997?

yanasidlinskiy · Answer

Or the other way around hahha.

ganeshie8 · Answer

1-0.997^5

yanasidlinskiy · Answer

Gotcha. Thanks thanks thanks. You're SUCH A LIFESAVER lol. Please. switch our brains!!!! I'm begging lol.

ganeshie8 · Answer

Haha ping me whenever such a technology becomes available :P

yanasidlinskiy · Answer

LOL.