Original practice · fully worked
Original variant: reverse conditioning for two certifications
Among technicians, 30% hold certification A and 40% hold certification B. Half of those with certification A also hold B. Find the probability that a technician holds A given that the technician holds B.
- A
0.250 - B
0.300 - C
0.375 - D
0.500 - E
0.750
Answer and calculation
The joint certification probability is 0.30(0.50)=0.15. Dividing by P(B)=0.40 gives 0.375, choice C.
Setup
Setup
The joint certification probability is the probability of certification A multiplied by the probability of certification B among those with A.
Pr(A∩B)=Pr(A)Pr(B∣A)=0.30(0.50)=0.15 Model
Model
To condition on certification B, divide the joint probability by the marginal probability of B.
Pr(A∣B)=Pr(B)Pr(A∩B) Compute
Compute
The joint probability is 0.15, and division by 0.40 gives 0.375.
Pr(A∣B)=0.400.15=0.375 Answer
Answer
The reverse conditional probability is 0.375.
0.375(C) 