Original practice · fully worked
Original variant: diagnostic signals
Every diagnostic batch produces at least one of three signals: drift D, latency L, or thermal T. Records show that P(D union T)=0.58 and P(D given L)=0.25. A latency signal and a thermal signal can never occur in the same batch. Calculate P(L).
- A
0.315 - B
0.420 - C
0.560 - D
0.580 - E
0.670
Answer and calculation
Because latency and thermal signals are mutually exclusive, the overlap of L with D union T is just D intersection L. The full-union equation becomes 1=b+0.58-0.25b, giving b=0.56 and choice C.
Setup
Setup
Write b for the latency probability. The conditional drift rate among latency batches determines their intersection.
Pr(D∩L)=Pr(L)Pr(D∣L)=0.25b Model
Model
Combine L with D union T. Since L and T are disjoint, their grouped overlap contains only D intersection L.
Pr(L∩(D∪T))=Pr(D∩L)=0.25b 1=Pr(L)+Pr(D∪T)−Pr(L∩(D∪T)) Compute
Compute
Insert the known union probability and solve the one-variable equation.
1=b+0.58−0.25b=0.58+0.75b b=0.750.42=0.56 Answer
Answer
The latency signal occurs in 56% of diagnostic batches.
Pr(L)=0.560(C) 