Original practice · fully worked
Original variant: redundant coolant pumps
A research freezer is kept cold by two redundant coolant pumps. Over the next service interval, pump A has failure probability 0.20 and pump B has failure probability 0.10, independently. At inspection the freezer is still being cooled, which means at least one pump is operating. Calculate the conditional probability that pump A is operating.
- A
0.800 - B
0.816 - C
0.900 - D
0.918 - E
0.980
Answer and calculation
Cooling continues with probability 1-(0.20)(0.10)=0.98. Pump A operates with probability 0.80 and that event guarantees cooling, so the conditional probability is 0.80/0.98=0.816327, choice B.
Setup
Setup
Let A and B denote the events that the corresponding pumps operate through the service interval.
Pr(A)=0.80,Pr(B)=0.90 Model
Model
Cooling is the union of the two operating events. Its complement requires both independent failures.
Pr(A∪B)=1−(0.20)(0.10)=0.98 Compute
Compute
Since an operating pump A necessarily implies cooling, normalize Pr(A) over the cooling event.
Pr(A∣A∪B)=0.980.80=0.8163265306… Answer
Answer
The conditional probability that pump A operates is approximately 0.816.
0.816(B) 