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
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 errorWe 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
orchestra answered 2 years agoRelated Solutions
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