A storeroom has two smoke detectors that work independently of each other…

Step 1. Both sound. $0.92 \times 0.85 = 0.782$.

Step 2. Exactly one sounds. The first sounds and the second is silent: $0.92 \times 0.15 = 0.138$. The second sounds and the first is silent: $0.08 \times 0.85 = 0.068$. The sum is $0.206$.

Step 3. At least one sounds. Both silent has probability $0.08 \times 0.15 = 0.012$. So the answer is $1 - 0.012 = 0.988$.