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HOME WORK – 4 Due: Monday, July 16th , 2018 (before class begins)

1. In an experiment to study the relationship of hypertension and smoking habits, the following data are collected for 180 individuals:

Nonsmokers Moderate Smokers Heavy Smokers

Hypertension 21 36 30

No hypertension 48 26 19

If one of these individuals is selected at random, find the probability that the person is

a. experiencing hypertension, given that the person is a heavy smoker; b. a nonsmoker, given that the person is experiencing no hypertension.

2. For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.25, the probability that the wife will vote on the referendum is 0.20. The

probability that a husband will vote on the bond referendum, given that his wife will vote, is 0.75.

What is the probability that

a. both husband and wife will vote? b. a wife will vote, given that her husband will vote? c. at least one member of a married couple will vote?

3. A large industrial firm uses three local motels to provide overnight accommodations for its clients. From past experience, it is known that 20% of the clients are assigned rooms at the

Ramada Inn, 50% at the Sheraton, and 30% at the Lakeview Motor Lodge. If the plumbing is

faulty in 5% of the rooms at the Ramada Inn, in 4% of the rooms at the Sheraton, and in 8% of

the rooms at the Lakeview Motor Lodge. Given that a client was assigned a room having faulty

plumbing, what is the probability that she was assigned accommodations at the Lakeview Motor

Lodge?

4. An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the

European project is successful. Suppose that A and B are independent events with 𝑷(𝑨) = 𝟎. 𝟒 and 𝑷(𝑩) = 𝟎. 𝟕.

a. If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning.

b. What is the probability that at least one of the two projects will be successful? c. Given that at least one of the two projects is successful, what is the probability that only

the Asian project is successful?

5. A particular airline has 10 A.M. flights from Chicago to New York, Atlanta, and Los Angeles. Let A denote the event that the New York flight is full and define events B and C analogously for

the other two flights. Suppose 𝑷(𝑨) = 𝟎. 𝟔, 𝑷(𝑩) = 𝟎. 𝟓, 𝑷(𝑪) = 𝟎. 𝟒 and the three events are independent. What is the probability that

a. all three flights are full? b. That at least one flight is not full? c. only the New York flight is full? d. That exactly one of the three flights is full?