Question

A computer program is tested by 5 independent tests. If there is an error, these tests will discover it with probabilities 0.1, 0.2, 0.3, 0.4, and 0.5respectively. Suppose that the program contains an error. What is the probability that it will be found 3. by at least one test? (Hint: this event is the complement of the event where the error is not found) 4. by all five tests?

Answer 1

ANSWER;

A computer program is tested by 5 independent tests. If there is an error, these tests will discover it with probabilities 0.1, 0.2, 0.3, 0.4, and 0.5respectively. Suppose that the program contains an error. What is the probability that it will be found 3. by at least one test? (Hint: this event is the complement of the event where the error is not found) 4. by all five tests.

a) THE PROBABILITY IS

P(found by 1st test) + P(1)*P(2nd) +  P(1)*P(2nd)*P(3rd) +  P(1)*P(2nd)*P(3rd)* P(4th) +  P(1)*P(2nd)*P(3rd)* P(4th) *P(5th)

.1 + (.1*.2) + (.1*.2*.3) + (.1*.2*.3*.4) + (.1*.2*.3*.4*.5)

.1296

b)AT LEAST ONE TEST

P(found by at least 1 test) - P(1st)

.1296 - .1 = .1196

c)BY ALL FIVE TESTS

P(1)*P(2nd)*P(3rd)* P(4th) *P(5th) = (.1*.2*.3*.4*.5) = 0.0012