During an epidemic of a certain disease a doctor is consulted by 110 people suffering from symptoms commonly associated with the disease. Of the 110 people, 45 are female of whom 20 actually have the disease and 25 do not. Fifteen males have the disease and the rest do not.

(a) A person is selected at random. The event that this person is female is denoted by A and the event that this person is suffering.

from the disease is denoted by B. Evaluate (i) P(A), (ii) P(AUB), (iii) P(An B), (iv) P(A|B).

(b) If three different people are selected at random without replacement, what is the probability of (i) all three having the disease, (ii) exactly one of the three having the disease, (iii) one of the three being a female with the disease, one a male with the disease and one a female without the disease?

(c) Of people with the disease 96% react positively to a test for diagnosing the disease as do 8% of people without the disease. What is the probability of a person selected at random (i) reacting positively, (ii) having the disease given that he or she reacted positively? (AEB)