Original practice · fully worked
Original variant: alpine telemetry links
A control center receives telemetry through a north link and a south link. Each link is available at the audit time with probability 0.85, and both are available with probability 0.75. If the south link is unavailable, calculate the probability that the north link is also unavailable.
- A
0.050 - B
0.150 - C
0.250 - D
0.333 - E
0.882
Answer and calculation
Inclusion–exclusion gives a 0.05 probability that both links are unavailable. The south link is unavailable with probability 0.15, so the conditional probability is 0.05/0.15=1/3, choice D.
Setup
Setup
Let U_N and U_S denote unavailability of the north and south links.
Pr(UN)=Pr(US)=0.15 Pr(UNc∩USc)=0.75 Model
Model
Use the availability information to find the lower-right cell of the two-link status table.
Pr(UN∩US)=1−0.85−0.85+0.75 Compute
Compute
Normalize the both-unavailable cell by the south-unavailable marginal probability.
Pr(UN∩US)=0.05 Pr(UN∣US)=0.150.05=31 Answer
Answer
The required conditional probability is approximately 0.333.
0.333(D) 