In a certain region of the country, it is known that the probability of selecting an adult over 50 years of age with cancer is 0.10. Thus, it is known that the probability of selecting an adult over 50 years of age without cancer is 0.90. GIVEN that a person does not have cancer, the probability of a doctor diagnosing this person as not having cancer is 0.75. GIVEN that a person over 50 does have cancer, the probability of a doctor diagnosing this person as not having cancer is 0.15. C: Person has cancer
C': Person does not have cancer
DH: Doctor diagnoses person as having cancer
DN: Doctor diagnoses person as NOT having cancer
PLEASE CARRY 4 DECIMAL PLACES AFTER THE DECIMAL POINT
FOR ALL CALCULATIONS for Questions 23 through 26.

a. What is the probability that a person over 50 years of age is diagnosed as NOT having cancer?
b. What is the probability that a person over 50 years of age is diagnosed as having cancer?
c. Given that a doctor diagnoses a person over 50 years of age as NOT having cancer, what is the probability that the person DOES HAVE cancer?
d. What is the probability that a person over 50 years of age DOES NOT have cancer AND they have been told by their doctor that they do not have cancer?