Question

You have been promoted to Intermediate Cat Herder! You now have a flock of 50 cats. They are a mixture of short haired cats and long haired cats, and you are preparing them for adoption. You observe that some of the cats are more prone to having hairballs than others, and you make a chart of this. What is the probability of a cat having a hairball, given that it is a long-haired cat?

	Hairball	No Hairball
Long Hair	20	8	28
Short Hair	10	12	22
	30	20	50

Briefly describe how you solved the previous question

Answer 1

Let A=event that a cat is having a hairball

B= event that a cat is a long haired cat

We know the following joint and marginal probabilities

The joint probability that a cat is having a hair ball and is a long-haired cat is

The marginal probability that a cat is a log-haired cat is

the conditional probability of a cat having a hairball (event A) , given that it is a long-haired cat (event B) is

ans:  the probability of a cat having a hairball, given that it is a long-haired cat is 0.7143