Question

In a class of 28 students, 21 have a cat and 9 have a dog. There are 7 students who have a cat and a dog. What is the probability that a student has a dog given that they do not have a cat?

Answer 1

$$P(Dog|\overline{Cat})=\dfrac{P(Dog\cap\overline{Cat})}{P(\overline{Cat})}$$

$$N(Dog\cap\overline{Cat)}=2$$

$$N(\overline{Cat)}=28-21=7$$

$$P(Dog|\overline{Cat})=\dfrac{2}{7}$$