In: Statistics and Probability
(1 point) 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 36% of all the families own a cat.
What is the probability that a randomly selected family owns a
dog?
What is the conditional probability that a randomly selected family
doesn't own a dog given that it owns a cat?
In a certain community, it is known that 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 36% of all families own a cat.
Let,
D= event that a family owns a dog
C=event that a family owns a cat.
Now, it is given,
Question a
What is the probability that a randomly selected family owns a dog ?
The answer is
Question b
What is the probability that a randomly selected family does not own a dog, given it owns a cat.
To find
By definition of conditional probability, this is
So, the probability that a family does not own a dog, given it owns a cat, is 0.77.