An electronic assembly consists of two sub-systems say A and B. From previous testing procedures, the following probabilities are assumed to be known. `P(A` fails`)=0.2`, `P(B` fails alone`)=0.15`, `P(A` and `B` Fail `)=0.15`. Evaluate the following probabilities: (i)`P(A` fails`/B` has failed `)` (ii) `P(A` fails alone`)`

Explanation

To solve the given problem step by step, we will evaluate the probabilities as requested.

### Given Information:
- \( P(A \text{ fails}) = 0.2 \)
- \( P(B \text{ fails alone}) = 0.15 \)
- \( P(A \text{ and } B \text{ fail}) = P(A \cap B) = 0.15 \)

### (i) To find \( P(A \text{ fails} | B \text{ has failed}) \):
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