A device has three parts P, Q and R, which work independently of one another with probabilities 0.9, 0.8 and 0.7 respectively. The device works if part P works and at least one of the parts Q and R works. The probability that the device works is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.846
Both Q and R fail with probability
\((1-0.8)(1-0.7) = 0.2\times 0.3 = 0.06\)
So at least one of Q and R works with probability
\(1-0.06 = 0.94\)
The device needs P to work as well. The parts are independent, so
\(P(\text{device works}) = 0.9\times 0.94 = 0.846\)
Why the other options are incorrect
Option (1) 0.504 — Incorrect. This is \(0.9\times 0.8\times 0.7\), the chance that all three parts work; the device also works when only one of Q and R works.
Option (3) 0.94 — Incorrect. This is only the chance that at least one of Q and R works; it leaves out part P.
Option (4) 0.994 — Incorrect. This is \(1-0.1\times 0.2\times 0.3\), the chance that at least one of the three parts works.