Exercise Problems for Probability 1. lfa letter is chosen at random from the English alphabet, nd the probability that the letter {a] is a vowel; {b} is listed somewhere before the letter]; {c} is listed somewhere after the letter g. 2. lf3 books are picked at random from a shelf containing5 novels, 3 books of poems, and a dictionary, what is the probability that {a} the dictionary is selected.?; {b} 2 novels and 1 book of poems are selected? 3. in a poker hand consisting of 5 cards, nd the probability of holding {a} 3 aces; {b} 4 hearts and 1 ciub 4. A pair of fair dice is tossed. Find the probability of getting {a} a total of 8: {b} at most a total of 5 5. Dom's Pizza Company uses taste testing and statisticai analysis of the data prior to marketing any new product. Consider a study involving three types of crust: {thin, thin with garlic and oregano. and thin with bits of cheese}. Dora's is also studying three sauces (standard, a new sauce with more garlic, and a new sauce with {rah basil]. {a} Hon:r many wmbinations of cmst and sauce are involved? {b} What is the probability that a judge will get a piain thin crust with a standard sauce for his first taste test? Exercise Problems for Conditional Probability 1. A. class in advanced physics is composed of 10 juniors, 30 seniors, and 10 graduate students. The nal grades show that 3 ofthe juniors, 1t] ofthe seniors, and 5 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A, what is the probability that he or she is a senior? 2. A random sample of 200 adults are classied below by sex and their level of education attained. Education Male Female Elementary 33 45 Secondary 28 5!] College 22 1? lfa person is picked at random from this group, nd the probability that {a} the person is a male, given that the person has a secondary education; {to} the person does not have a college degree, given that the person is a female. 3. in the senior year of a high school graduating class of 100 student, 42 studied mathematics, 58 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematits and psychology, '3' studied history but neither mathematics nor psychology, 1t] studied all three subject, and 3 did not take any of the three. Randomly select a student from the class and nd the probabilities of the following event. {a} A person enrolled in psychology takes all three subjects. {b} A person not taking psychology is taking both history and mathematics. 4. The probability that a doctor correctly diagnoses an illness is 03'. Given that the doctor makes an incorrect diagnosis, the probability that the patient les a lawsuit is 0.9. What is the probability that the doctor makes an incorrect diagnosis and the patient sues? 5. A town has two re engines operating independently. The probability that a specic engine is available when needed is 0.96. {a} What is the probability that neither is available when needed? {b} What is the probability that a re engine is available when needed? Exercise Problems for Bayes Theorem 1. In a certain region ofthe country it is known from past experience that the probabilityof selecting an adult overdDyears of age with cancer is 0.05. If the probability ofa doctor correctly diagnosing a person with cancer as having the disease is 0.?3 and the probability of inoorrectly diagnosing a person without cancer as having the disease is 0.06, what is the probability that a} an adult over 40 years of age is diagnosed as having canoer?; b) a person diagnosed as having cancer has the disease? 2. Police plan to enforce speed lim'rE by using radar traps at four different locations within the city limits. 111e radar traps at each of the locations L1, L1, L3, and ngill be operated 40%, 30%, 20%, and 30% of the time. lfa person who is speeding on her way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that a} she will receive a speeding ticket? b} she passed through the radar trap located at L2 at received a speeding ticket on her way to work? 3. A paintstore chain produoa and sells latex and semigloss paint. Based on longrange sales, the probability that a customer will purchase latex paint is 0.?5. Of those that purchase latex paint, 60% also purchase rollers. But only 30% of semigloss paint buyers purchase rollers. A randomly selected buyer purchases a roller and a can of paint. What is the probability that the paint is latex? 4. Suppose that the four inspectors at a lm factory are supposed to stamp the expiration date on each package of lm at the end of the assembly |ine.John, who stamps 20%of the packages, fails to stamp the expiration date once in every 200 packages; Tom, who stamps 60% of the packages, fails to stamp the expiration date onoe in every 100 package; jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages; and Pat, who stamps 5% of the packages, fails to stamp the expiration date once in every 200 packages. If a customer complains that her package offilm does not show the expiration date, what is the probability that it was inspected by John