There are 1000 residents in a community. Among the 1000 residents, 800 residents have a cat, and 300 residents have a dog. 250 residents have both pets.
a) What is the probability that a randomly selected resident has neither pet?
b) What is the probability that a randomly selected resident has a cat, given that he/she has a dog?
c) Let event A be the selected resident having a cat, and event B be the selected residents having a dog. Are A and B independent events? Why or why not?
(PLEASE SHOW YOUR WORK) - Thank you!