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

P(found by at least one test)=0.72

Explanation:

Before to get started we are going to define each single error found by each test and their respective probabilities

a= error found by test 1 P(a)=0.2 P(not a)=0.8

b= error found by test 2 P(b)=0.3 P(not b)=0.7

c=error found by test 3. P(d)=0.5 P(not c)=0.5

In order to find the probabilities that an error will be found by at least one test, firstly we have to compute the probability of not finding any error by any test.

Since the tests are independent each them were are going to compute this probability through the following way:

P(not a)*P(not b)*P(not c)=0.8*0.7*0.5=0.28

P(found by at least one test) =1-P(not found by any test)=1-0.28

P(found by at least one test)=0.72