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1. Probability Concepts 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  D, W  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? .

1. Probability Concepts
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
nd 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?

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1. GOAL STATEMENT: Please complete the following goal statement in the space provided or by submitting a separate typed document. If submitting the statement in another format, please indicate such in the box below.The statement should be at least one type written page in length or 200+ words. Future Goals: Identify your career/professional goals. How will this graduate degree facilitate these goals? Leadership or Group Contributions: Describe examples of your leadership experience in which you have significantly influenced others, helped resolve disputes, or contributed to group efforts over time. Write an essay (in English) on how this degree supports the candidate’s academic and career aspirations. .

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