at least one of the tests gives the correct result

hi,

There are two tests for a particular antibody. Test A gives a correct result 95% of the time. Test B is accurate 89% of the time. If a patient is given both tests, find the probability that at least one of the tests gives the correct result.

I thought it was .95 * .89, but I thought wrong..help please?

Thanks for the help.

Havent had stats in years, but here's what I remember: P(at least 1 is correct) = 1-P(none are correct)

What is the probability that neither are correct? It is the Probability that the first test is incorrect AND the second test is incorrect. P(first is incorrect)=0.05, and P(second is incorrect) = 0.11.

P(first is incorrect AND second is incorrect) = P(first is incorrect) * P( second is incorrect) = 0.05 * 0.11 = 0.0055.

1-0.0055 = 0.9945.

Alternatively you could have done:
P(At least one of the two is correct) = P(first is correct OR second is correct) = P(first is true) + P(second is true) - P(first is true and second is true) = 0.95 + 0.89 - 0.95*0.89 = 1.84-.8455 = 0.9945

-daon

The opposite of 'at least one' is none. So, find the probability that neither test works and subtract from 1.

1-(0.05)(0.11)=0.9945=99.45%


EDIT: Daon, you beat me to the draw, but our solutions jive.

okay thanks
wow you guys are like 2 mins apart in responding