In a very large apartment building in New York 75% of residents have a pet. In that same apartment building 30% are over the age of 65 years. It is also the case that 23% of the residents have a pet and are over the age of 65 years.

a. What is the probability that if I sampled a single resident that individual would have a pet or be over the age of 65 years? Show the work/expressions that lead to the answer. I don't need the intermediary arithmetic calculations. Use function notation to indicate what you are calculating. Write the probability to four decimal places.

b. What is the probability that a person chosen randomly is not over the age of 65 and has a pet? Show the work/expressions that lead to the answer. I don't need the intermediary arithmetic calculations. Use function notation to indicate what you are calculating. Write the probability to four decimal places.

c. Of the people over the age of 65, what is the probability that a person chosen randomly in that apartment building, does not have a pet?

Show the work/expressions that lead to the answer. I don't need the intermediary arithmetic calculations. Use function notation to indicate what you are calculating. Write the probability to four decimal places.