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%

Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event that an animal is a dog and \(B\) be the event that an animal is spotted.

Step2: Substitute the given values

We are given that \(P(A) = 38\%=0.38\), \(P(B)=40\% = 0.4\), and \(P(A\cap B)=12\%=0.12\).
Substitute these values into the formula: \(P(A\cup B)=0.38 + 0.4-0.12\).

Step3: Calculate the result

First, add \(0.38\) and \(0.4\): \(0.38+0.4 = 0.78\). Then subtract \(0.12\) from \(0.78\): \(0.78-0.12=0.66\).

Answer:

B. \(66\%\)