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In a certain community, 36 percent of the families own a
Chapter 3, Problem 17P(choose chapter or problem)
In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is
(a) the probability that a randomly selected family owns both a dog and a cat?
(b) the conditional probability that a randomly selected family owns a dog given that it owns a cat?
Questions & Answers
QUESTION:
In a certain community, 36 percent of the families own a dog and 22 percent of the families that own a dog also own a cat. In addition, 30 percent of the families own a cat. What is
(a) the probability that a randomly selected family owns both a dog and a cat?
(b) the conditional probability that a randomly selected family owns a dog given that it owns a cat?
ANSWER:
Step 1 of 2
(a)
We are asked to find the probability that a randomly selected family owns both a dog and a cat.
Let be the event a family owns a dog, and
be the event that a family owns a cat.
We need to find
The probability that a family owns a dog is given,
The probability that a family owns a cat is given,
The probability that a family own a dog also own a cat is given,
By the conditional probability formula, we can write
Hence the probability that a randomly selected family owns both a dog and a cat is