Final answer:
The probability of the system of three components in series working is found by multiplying their individual probabilities: 0.92 * 0.95 * 0.88, which equals 0.76936 or 76.936%.
Step-by-step explanation:
The question is about calculating the probability that a system of three components in series will work. Each component has its own individual probability of working: 0.92 for the first, 0.95 for the second, and 0.88 for the third. To find the system's probability of working, you multiply the probabilities of each component because they are in series:
- Probability of the first component working (P1) = 0.92
- Probability of the second component working (P2) = 0.95
- Probability of the third component working (P3) = 0.88
Thus, the total system probability (Psystem) of working:
Psystem = P1 * P2 * P3
= 0.92 * 0.95 * 0.88
= 0.76936
The probability of the system working is 0.76936, which can also be expressed as 76.936%.