Question

A veterinarian surveys her clients and finds that 32 percent of the households have dogs, 25 percent have cats, and 11 percent have both dogs and cats. Let event C be choosing a client who has cats and let event D be choosing a client who has dogs. Which statements are true? Check all that apply.

P(C | D) = 0.78
P(D | C) = 0.44
P(C ∩ D) = 0.11
P(C ∩ D) = P(D ∩ C)
P(C | D) = P(D | C)

Answer 1

Compute from P(D)=0.32, P(C)=0.25, P(C ∩ D)=0.11.

- P(C | D) = 0.11/0.32 = 0.34375, so P(C | D) = 0.78 is false.
- P(D | C) = 0.11/0.25 = 0.44, so P(D | C) = 0.44 is true.
- P(C ∩ D) = 0.11 is true.
- P(C ∩ D) = P(D ∩ C) is true (intersection is commutative).
- P(C | D) = P(D | C) is false (0.34375 ≠ 0.44).

True statements: P(D | C) = 0.44; P(C ∩ D) = 0.11; P(C ∩ D) = P(D ∩ C).