In Mr. Smeed's third period class, 22 students have dogs for pets, and 18 have cats.

a. If there are 32 students in the class, and all students have at least one pet, how many have both a dog and a cat?

b. If a student is chosen at random from Mr. Smeed's class, what is the probability that the student has a dog for a pet?

c. Patricia is in Mr. Smeed's class and has a cat for a pet. What is the probability that she also has a dog?