Independent solution

How to solve this Inclusion-Exclusion question

Setup

Setup

Convert the stated probabilities into counts among the 200 customers. The number buying at least one item is the complement of the no-purchase group.

n(C∪S)=200(1−0.60)=80n(C\cup S)=200(1-0.60)=80
n(C)=200(0.20)=40,n(S)=200(0.35)=70n(C)=200(0.20)=40,\qquad n(S)=200(0.35)=70

Model

Model

Use inclusion-exclusion to determine the joint group, then subtract it from each marginal group.

n(C∩S)=40+70−80=30n(C\cap S)=40+70-80=30
n(C only)=40−30=10n(C\text{ only})=40-30=10
n(S only)=70−30=40n(S\text{ only})=70-30=40

Compute

Compute

A joint purchase has undiscounted price 400 and discounted price 360. Add revenue across the three purchasing groups.

0.90(300+100)=3600.90(300+100)=360
R=10(300)+40(100)+30(360)R=10(300)+40(100)+30(360)
R=17,800R=17{,}800

Answer

Answer

The total revenue is 17,800.

17,800(B)\boxed{17{,}800\quad\text{(B)}}