Probability ques

[hopeful786]

a nw tst fr detect pros canc is neg in 95% of ptx who do not have the disease. If the tst is usde wth 8 consecutive bld sample taken from ptx without the dsesas, wht is the prob of getting at lest one post tst rslt?

appologize for the misspels...

[rose.82]

Hi,

I thinke the prob of getting at lest one positive test is:
5%+5%+5%+5%+5%+5%+5%+5%=40%

[hopeful786]

close to the actual answer but not the right step
I ll wait for others and then post...

[E2O]

5 to the power 8
sorry dont kn how to use the super script

[hopeful786]

The answer is

1-(0.95^8)

You have to multiply because the events are independent.

I thought also to go the 0.5^8 route however it gives a very small probability when I actually calculated it, but I still don't know why this is wrong.

Anyone can enlighten us?

[rose.82]

Hi,
Oh, yes you are right 1-(.95^8)
Because you want at least one test positive ,it means 1 positive or 2 positive or 3 positive,... .
(.95^8) means all cases are negative and 1-(.95^8) means you calculate all situations except all negative.
You can't use 0.5^8 because this means all tests positive not at least one positive.

[hopeful786]

Okay now it makes sense, thnx.
At least one test positive

so
0.95^8 = prob All test are negative.
0.05^8 = prob All test are positive.
1-(0.95^8) = prob of 1 or more positives.
1-(0.05^8) = prob of 1 or more negatives.