In a certain community, 30% of the families own a dog, and 20% of the families that own a dog also own a cat. it is also known that 34% of all the families own a cat. what is the probability that a randomly selected family owns a cat? what is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

the answer is 58.8%

Step-by-step explanation:

From the example given, we apply the use of conditional probability

The general rule for conditional probability is: P(A given B) = Probability of (A and B) / Probability (B).

The Probability of a randomly select family owns a cat is 34%.

The Probability of not owing a dog (A), given that it owns a cat (B) = P(not owing a dog AND owning a cat) / P (owning a cat). which is = x/y so

The relationship between a Cat and Dog is not determined  to be independent, thus, we say x just by finding the probability of the two events and multiplying.

Given that 30% own a dog and 20% of those own a cat is 30% x 20% = 6%

7% of all the families own both.

Since 34% own a cat, 34 - 6 = 28% own a cat but not a dog. That gives you x, and y is still just 34%,

So for x/y = 20/34

= 58.8%