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%
Answer and calculation
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.
{(r,s):r+s≥6}={(2,4),(3,3),(4,2),(3,4),(4,3),(4,4)} Compute
Compute
Multiply the independent weights for each ordered pair and add.
Pr(R+S≥6)=1022⋅2+4⋅4+2⋅2+4⋅2+2⋅4+2⋅2 Pr(R+S≥6)=10044=0.44 Answer
Answer
The chance of delivering at least six parcels is 0.44.
0.44(E) 