Answer to Question #329959 in Statistics and Probability for nice short

Question

: A computer program is tested by 3 independent tests. When there is an error, these tests will

discover it with probabilities 0.2, 0.3 and 0.5, respectively. Suppose that the program contains an

error. What is the probability that it will be found by at least one test.

Answer 1

let A =error found by test 1

let B=error found by test 2

let C=error found by test 3

Given P(A)=0.2, P(B)=0.3, P(C)=0.5

therefore P(notA)=0.8, P(notB)=0.7, P(notC)=0.5

Note: tests are independent P(notA & notB & notC)=P(notA)*P(notB)*P(notC)=0.8 $\cdot$ 0.7$\cdot$0.5=0.28

P(found by at least one test)= 1- P(not found by any test)=1-P(notA & notB & notC)=1-0.28=0.82