Answer to Question #124838 in Statistics and Probability for Yasini

Question

A computer program is tested by three independent tests. When there is an error these tests will discover it with probabilities 0.2, 0.3, 0.5 respectively. Suppose that the program contain 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*0.7*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