This Exam P sample reference tests Inclusion–Exclusion. Completing the six-cell table shows that the irregular-and-low cell is 0.02, so the regular-and-low cell is 0.20, choice E.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AThe value 2% is the irregular-and-low cell. The question asks for the complementary regular cell within the 22% low column.
BThe value 5% is the irregular-and-high cell obtained from 0.15/3, not the requested regular-and-low cell.
CThe value 8% is the irregular-and-normal cell obtained from 0.64/8, not the requested cell.
Original practice · fully worked
Original variant: complete a two-by-two service table
Seventy percent of support tickets are submitted by subscribed customers, 40% are priority tickets, and 30% are both subscribed and priority. What proportion are submitted by subscribed customers but are not priority tickets?
A 0.10
B 0.30
C 0.40
D 0.60
E 0.70
Variant answer in brief
Subtracting the joint cell from the subscribed marginal leaves 0.40, choice C.
Setup
Setup
Partition the subscribed-customer event S into priority and nonpriority tickets.
S=(S∩P)∪˙(S∩Pc)
Model
Model
Because the two cells are disjoint, subtract the subscribed-and-priority cell from the subscribed marginal to isolate subscribed nonpriority tickets.
Pr(S∩Pc)=Pr(S)−Pr(S∩P)
Compute
Compute
The required probability is 0.70-0.30=0.40.
Pr(S∩Pc)=0.70−0.30=0.40
Answer
Answer
Thus 40% of tickets are submitted by subscribed customers and are not priority, which is choice C.
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
