Question

Three independent diagnostic tests T1, T2, T3 are run on the same patient. The probabilities that these tests will give correct results are respectively: 90%, 85%, 80%. What is the probability that at least one test will result in error?

Please explain :)

Answer 1

Solution:

   We are given that: Three independent diagnostic tests T1, T2, T3 are run on the same patient.

. The probabilities that these tests will give correct results are:

P(T1) =0.90

P(T2) =0.85

P(T3) = 0.80

We have to find: the probability that at least one test will result in error?

P( At least one test will result in Error ) = .......?

P( At least one test will result in Error ) = 1 - P( None of the test will result in Error)

P( At least one test will result in Error ) = 1 - P( All of the test will correct results)

P( At least one test will result in Error ) = 1 - [ P(T1) x P(T2) x P(T3) ]

We do multiplication of probabilities, since Three tests are independent.

P( At least one test will result in Error ) = 1 - [ 0.90 x 0.85 x 0.80 ]

P( At least one test will result in Error ) = 1 - 0.612

P( At least one test will result in Error ) = 0.388