Original practice · fully worked
Original variant: source inference from two repeated signals
A monitoring source is type A with probability 0.25 and type B otherwise. On each independent trial it emits a red signal with probability 0.60 if type A and 0.20 if type B. Two consecutive red signals are observed. Find the posterior probability of type A.
- A
0.250 - B
0.750 - C
0.600 - D
0.500 - E
0.900
Answer and calculation
The two-red weights are 0.25(0.60²)=0.09 and 0.75(0.20²)=0.03. Type A therefore has posterior probability 0.75, choice B.
Setup
Setup
For each source type, multiply its prior probability by the conditional likelihood of two consecutive red signals.
wA=0.25(0.60)2=0.09 wB=0.75(0.20)2=0.03 Model
Model
Normalize the type-A two-red weight by the sum of the type-A and type-B weights.
Pr(A∣RR)=wA+wBwA Compute
Compute
The weights are 0.09 and 0.03, so the posterior probability of type A is 0.09/(0.09+0.03)=0.75.
Pr(A∣RR)=0.09/0.12=0.75 Answer
Answer
Given two red signals, the source is type A with probability 0.75, which is choice B.
0.75(B) 