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.

This Question is not complete because it lacks the appropriate options

Complete 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.

1. P(C | D) = 0.78

2. P(D | C) = 0.44

3. P(C ∩ D) = 0.11

4. P(C ∩ D) = P(D ∩ C)

5. P(C | D) = P(D | C)

3. P(C ∩ D) = 0.11

4. P(C ∩ D) = P(D ∩ C)

Step-by-step explanation:

Clients that have Cats = P(C) = 25% = 0.25

Clients that have Dogs = P(D) = 32% = 0.32

The number of Clients that have Dogs and Cats = P(D ∩ C) = 11% = 0.11

Sets of data in mathematics are governed by laws which include Distributive law, Commutative law, Associative law, Identity law e.t.c.

The commutative law of sets states that :

A ∩ B = B ∩ A

A ∪ B = B ∪ A

Therefore, based on the commutative law of sets, Option 4 " P(C ∩ D) = P(D ∩ C) " is correct.

Since we are told in the question above that the number of Clients that have Dogs and Cats = P(D ∩ C) = 11% = 0.11 and based on the commutative law that says

P(C ∩ D) = P(D ∩ C)

Therefore, Option 3 " P(C ∩ D) = 0.11"

is correct as well.

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step-by-step explanation:

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