Question

• 38% of the animals are dogs.
• 40% of the animals are spotted.
• 12% of the animals are spotted dogs.
What percent of the animals in the store are spotted or dogs?
A. 54%
B. 66%
c. 78%
D. 80%

Answer 1

To find the percentage of animals that are either spotted or dogs, we can use the principle of inclusion-exclusion.

Let:
- \( P(D) \) be the percentage of dogs = 38%
- \( P(S) \) be the percentage of spotted animals = 40%
- \( P(D \cap S) \) be the percentage of spotted dogs = 12%

We want to find \( P(D \cup S) \), the percentage of animals that are either dogs or spotted. The formula for inclusion-exclusion is:

\[
P(D \cup S) = P(D) + P(S) - P(D \cap S)
\]

Substituting in the known values:

\[
P(D \cup S) = 38\% + 40\% - 12\%
\]

Calculating this gives:

\[
P(D \cup S) = 38 + 40 - 12 = 66\%
\]

Thus, the percentage of animals in the store that are spotted or dogs is **66%**.

The correct answer is **B. 66%**.