A machine works only if all three of its parts work. The three parts work independently of one another with probabilities 0.9, 0.8 and 0.75 respectively. The probability that the machine works is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.54
The machine works when the first, the second and the third part all work. The parts are independent, so the probabilities are multiplied:
\(P(\text{machine works}) = 0.9\times 0.8\times 0.75\)
\(P(\text{machine works}) = 0.72\times 0.75 = 0.54\)
Why the other options are incorrect
Option (1) 0.46 — Incorrect. This is 1 − 0.54, the probability that the machine does not work.
Option (3) 0.995 — Incorrect. This is \(1-0.1\times 0.2\times 0.25\), the probability that at least one part works.
Option (4) 0.005 — Incorrect. This is \(0.1\times 0.2\times 0.25\), the probability that all three parts fail.