Question

In a certain community, 24% of the families own a dog, and 25% of the families that own a dog also own a cat. It is also known that 36% of all the families own a cat.

What is the conditional probability that a randomly selected family owns a dog given that it doesn't own a cat?

Answer 1

P(Dog) = 0.24

P(cat | dog) = 0.25

P(Cat) = 0.36

Using multiplication rule,

P( Cat AND Dog) = P(cat | dog) * P(Dog)

= 0.25 * 0.24

= 0.06

We have to calculate, P(Dog | Cat^c ) = ? [ Where Cat^c represents NOT cat ]

P(Dog | Cat^c ) = P(Dog AND Cat^c ) / P(Cat)^c

= [ P(Dog) - P( Cat AND Dog) ] / ( 1 - P(Cat) )

= [ 0.24 - 0.06] / ( 1 - 0.36 )

= 0.2813