Question

In a certain community, 40% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 28% of all the families own a cat. What is the probability that a randomly selected family owns both a dog and a cat? What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?

Name: in a certain community 40 of the families own a dog and 20 of the families that own a dog also own a cat it is also known that 28 of all the families own a cat what is the probability that a 77682
Uploaded: 2022-05-31T02:50:54-08:00
Duration: 3 min 7 s
Channel: Adi S
Description: in a certain community 40 of the families own a dog and 20 of the families that own a dog also own a cat it is also known that 28 of all the families own a cat what is the probability that a 77682

          In a certain community, 40% of the families own a dog, and 20%
of the families that own a dog also own a cat. It is also known
that 28% of all the families own a cat. 
What is the probability that a randomly selected family owns both a
dog and a cat?  
What is the conditional probability that a randomly selected family
doesn't own a dog given that it owns a cat?

Added by Matthew R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

05/31/2022

Step 1

Given: - Probability of owning a dog (B) = 0.4 - Probability of owning a cat given that they own a dog (C|B) = 0.2 Using the formula for the probability of the intersection of two events: \[ P(B \cap C) = P(C|B) \times P(B) \] Substitute the given values: \[ Show more…

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In a certain community, 40% of the families own a dog, and 20% of the families that own a dog also own a cat. It is also known that 28% of all the families own a cat. What is the probability that a randomly selected family owns both a dog and a cat? What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?