Question

researchers recorded data on pet ownership for randomly selected households in a large city. the venn diagram summarizes the data using events c: has a cat and d: has a dog.
if a household that owns a cat is selected at random, what is the probability that the household owns a dog?
(round to 4 decimal places. leave your answer in decimal form.)

Explanation:

Step1: Recall the formula for probability of event D

The probability of event \(D\) (has a dog) is the sum of the probability of only \(D\) and the probability of the intersection of \(C\) and \(D\). Let \(P(D)\) be the probability of having a dog. From the Venn - diagram, the area representing only \(D\) is \(0.22\) and the area of the intersection of \(C\) and \(D\) is \(0.15\).

Step2: Calculate \(P(D)\)

Using the formula \(P(D)=\text{Only }D+\text{Intersection of }C\text{ and }D\). Substitute the values: \(P(D)=0.22 + 0.15\).

Answer:

\(0.37\)