This Exam P sample reference tests Discrete Random Variables. This is a discrete convolution for two independent copies of the hourly count. Adding the six qualifying ordered-pair probabilities gives 57/400, so the official answer is choice E.
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AThis counts only outcomes in which both technicians resolve at least four problems. It omits the qualifying ordered pairs (3,5) and (5,3).
BThis total counts each unequal qualifying pair in only one order. The technicians are distinguishable, so both (x,y) and (y,x) must be retained.
CThis is the probability of exactly eight resolved problems, obtained from (3,5), (4,4), and (5,3), rather than the probability of at least eight.
DThis counts qualifying outcomes having at least one count equal to five, but it leaves out the additional qualifying outcome (4,4).
Original practice · fully worked
Original variant: two-drone parcel sortie
Two rescue drones independently complete a parcel sortie. The number delivered by either drone has probabilities 0.10, 0.10, 0.20, 0.40, and 0.20 for counts 0, 1, 2, 3, and 4, respectively. Calculate the probability that the two drones deliver at least six parcels in total.
A 24%
B 28%
C 32%
D 36%
E 44%
Variant answer in brief
Enumerating the ordered count pairs with total at least six gives probability 0.44. The result selects choice E.
Setup
Setup
Let R and S be the parcel counts for the first and second drone. Their common probability weights for counts zero through four are 1, 1, 2, 4, and 2 out of 10.
Pr(R=k)=Pr(S=k)=10(1,1,2,4,2)k,k=0,1,…,4
Model
Model
The qualifying ordered pairs are those with a sum of six, seven, or eight.
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.
