Question

Suppose that the four Software Quality Assurance inspectors at a software-house are to check software bugs in each module for a software developed. Zaid, who checks 20% of the modules, fails to identify a bug in every 200 modules: Bakar, who checks 60% of the modules, fails to identify a bug in every 100 modules; Sara, who checks 15% of the modules, fails to identify a bug in every 90 modules; and Zara, who checks 5% of the modules, fails to identify a bug in every 200 modules. 1200 If a bug is found in the software, what is the probability that it came from the module inspected by Zaid?

Answer 1

To find the probability that the bug came from the module inspected by Zaid, we can use conditional probability. Based on the given information, we can calculate the probability of Zaid not finding a bug in a module. Then, using Bayes' theorem, we can calculate the probability that a bug came from the module inspected by Zaid. The probability is approximately 0.182, or 18.2%.

Step-by-step explanation:

To find the probability that the bug came from the module inspected by Zaid, we need to use conditional probability. Let's define some variables:

A: Event that a bug is found in the software.

B: Event that the bug came from the module inspected by Zaid.

Based on the information given, we can calculate the probability of each inspector failing to identify a bug in a module:

P(Zaid not finding a bug) = 1 / 200 = 0.005

P(Bakar not finding a bug) = 1 / 100 = 0.01

P(Sara not finding a bug) = 1 / 90 ≈ 0.0111

P(Zara not finding a bug) = 1 / 200 = 0.005

Now, let's calculate the probability that a bug came from the module inspected by Zaid using Bayes' theorem:

P(B|A) = (P(A|B) * P(B)) / P(A)

We are given that Zaid inspects 20% of the modules, so P(B) = 0.20. P(A|B) is the probability of finding a bug in the module inspected by Zaid, which is 1 - P(Zaid not finding a bug) = 1 - 0.005 = 0.995. To calculate P(A), we need to consider the probabilities of finding a bug in any module, which can be calculated as:

P(A) = P(A|B) * P(B) + P(A|not B) * P(not B) = 0.995 * 0.20 + 0.01 * 0.60 + 0.0111 * 0.15 + 0.005 * 0.05

Finally, substituting the values into Bayes' theorem:

P(B|A) = (0.995 * 0.20) / (0.995 * 0.20 + 0.01 * 0.60 + 0.0111 * 0.15 + 0.005 * 0.05) ≈ 0.182

Therefore, the probability that the bug came from the module inspected by Zaid is approximately 0.182, or 18.2%.