[Gorata]

During an epidemic of disease,
a doctor sees 110 people who have symptoms commonly associated with the
disease. Of these, 45 are women, of whom 20 actually have the disease. 15 of
the men also have the disease. Suppose a
person is selected at random from those with symptoms seen by the doctor. Define events:

W: the
selected person is a woman

D: the
selected person has the disease
(a)draw a Venn diagram for this problem
(b) Describe in words the events W, W È D, W Ç D, and W|D, and compute
probabilities associated with each of these events
(c) If three people are selected at random, what is the probability that
(I) all three of them have the disease
(ii)exactly one of them has the disease?
(d) Of people with the disease, 95% react positively to a diagnostic test, as also do 8% of people without the
disease. What is the probability of a person selected at random
(a) reacting positively
(b) having the disease given that he or she reacted positively?