Question

In: Statistics and Probability

A computer program is tested by 5 independent tests. If there is an error, these tests...

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 0.5, respectively. Suppose that the program contains an error. What is the probability that it will be found
a. by at least one test?
b. by at least two tests?
c. by all five tests?

Solutions

Expert Solution

Let

  • A=event that the first test finds the error
  • B=event that the second test finds the error
  • C=event that the third test finds the error
  • D=event that the fourth test finds the error
  • E=event that the fifth test finds the error

and the complement events

  • event that the first test does not find the error
  • event that the second test does not find the error
  • event that the third test does not find the error
  • event that the fourth test does not find the error
  • event that the fifth test does not find the error

We know the following probabilities

a. by at least one test?

The probability that it will be found by no test is

The probability that it will be found by at least one test is

ans: The probability that it will be found by at least one test is 0.8488

b. The probability that it will be found by no test is 0.1512 (from part a)

The probability that it will be found by exactly 1 test is

Finally, The probability that it will be found by at least two tests is

ans: The probability that it will be found by at least two tests is 0.4774

c. by all five tests?

The probability that it will be found by all five tests is

ans: The probability that it will be found by all five tests is 0.0012



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