Problem # 10):
A large research hospital has accumulated statistical data on its patients for an extended period. Researchers have determined that patients who are smokers have an 18% chance of contracting a serious illness such as heart disease, cancer, or emphysema, whereas there is only a .06 probability that a nonsmoker will contract a serious illness. From hospital records, the researchers know that 23% of all hospital patients are smokers, while 77% are nonsmokers. For planning purposes, the hospital physician staff would like to know the probability that a given patient is a smoker if the patient has a serious illness.
Problem # 12):
The Senate consists of 100 senators, of whom 34 are Republicans and 66 are Democrats. A bill to increase defense appropriations is before the Senate. Thirty- five percent of the Democrats and 70% of the Republicans favor the bill. The bill needs a simple majority to pass. Using a probability tree, determine the probability that the bill will pass.
Problem # 14):
A metropolitan school system consists of three districts— north, south, and central. The north dis-trict contains 25% of all students, the south district contains 40%, and the central district contains 35%. A minimum- competency test was given to all students; 10% of the north district students failed, 15% of the south district students failed, and 5% of the central district students failed.
a. Develop a probability tree showing all marginal, conditional, and joint probabilities.
b. Develop a joint probability table.
c. What is the probability that a student selected at random failed the test?