Exam 4: Introduction to Probability

A random sample of computer users was asked which browser they primarily relied on for surfing the Internet and whether this browser was installed on a PC or on a Mac computer. The following contingency table shows these results. Given that the randomly selected computer was a PC, the probability that the computer used the Firefox browser is ________.

Probabilities can be expressed as fractions, percentages, and ________.

Romi, a production manager, is trying to improve the efficiency of his assembly line. He knows that the machine is set up correctly only 60% of the time. He also knows that if the machine is set up correctly, it will produce good parts 80% of the time, but if set up incorrectly, it will produce good parts only 20% of the time. Romi starts the machine and produces one part before he begins the production run. He finds the first part to be good. What is the revised probability that the machine was set up correctly?

The complement of an event A, within the sample space S, is the event consisting of ________.

A company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25. Winning project A and winning project B are independent events. What is the probability that the company does not win either project?

The following contingency table provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older. Here xx and yy represent missing values. Compute the probability that an individual is under 35 and prefers running.

Restaurants in London, Paris, and New York want diners to experience eating in pitch darkness to heighten their senses of taste and smell (Vanity Fair, December 2011). Suppose 400 people were asked, "If given the opportunity, would you eat at one of these restaurants?" The accompanying contingency table, cross-classified by age, would be produced. a. What is the probability that a respondent would eat at one of these restaurants? B) What is the probability that a respondent would eat at one of these restaurants or is in the 30-44 age bracket? C) Given that the respondent would eat at one of these restaurants, what is the probability that he or she is in the 30-44 age bracket? D) Is whether a respondent would eat at one of these restaurants independent of one's age? Explain using probabilities.

As part of pharmaceutical testing for drowsiness as a side effect of a drug, 200 patients are randomly assigned to one of two groups of 100 each. One group is given the actual drug and the other a placebo. The number of people who felt drowsy in the next hour is recorded as a. What is the probability that a randomly picked patient in the study feels drowsy in the next hour? B) What is the probability that a randomly picked patient in the study takes the placebo or feels drowsy in the next hour? C) Given that the patient was given the drug, what is the probability that he or she feels drowsy in the next hour? D) Is whether a patient feels drowsy independent of taking the drug? Explain using probabilities.