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An economist says that the probability is \(.47\) that a randomly selected adult is in favor of keeping the Social Security system as it is, \(.32\) that this adult is in favor of totally abolishing the Social Security system, and .21 that this adult does not have any opinion or is in favor of other options. Were these probabilities obtained using the classical approach, relative frequency approach, or the subjective probability approach? Explain your answer.

A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is a. red? b. green?

A die is rolled once. What is the probability that a. a number less than 5 is obtained? b. a number 3 to 6 is obtained?

A random sample of 2000 adults showed that 1320 of them have shopped at least once on the Internet. What is the (approximate) probability that a randomly selected adult has shopped on the Internet?

In a group of 50 car owners, 8 own hybrid cars. If one car owner is selected at random from this group, what is the probability that this car owner owns a hybrid car?

Jane and Mike are planning to go on a two-week vacation next summer. They have selected six vacation resorts, two of which are in Canada and remaining four are in Caribbean countries. Jane prefers going to a Canadian resort, and Mike prefers to vacation in one of the Caribbean countries. After much argument, they decide that they will put six balls of the same size, each marked with one of the six vacation resorts, in a hat. Then they will ask their 8 -year- old son to randomly choose one ball from these six balls. What is the probability that a vacation resort from the Caribbean countries is selected? Is this an example of the classical approach, relative frequency approach, or the subjective probability approach? Explain your answer. Do these probabilities add to \(1.0 ?\) If yes, why?

A sample of 400 large companies showed that 130 of them offer free health fitness centers to their employees on the company premises. If one company is selected at random from this sample, what is the probability that this company offers a free health fitness center to its employees on the company premises? What is the probability that this company does not offer a free health fitness center to its employees on the company premises? Do these two probabilities add to \(1.0 ?\) If yes, why?

In a large city, 15,000 workers lost their jobs last year. Of them, 7400 lost their jobs because their companies closed down or moved, 4600 lost their jobs due to insufficient work, and the remainder lost their jobs because their positions were abolished. If one of these 15,000 workers is selected at random, find the probability that this worker lost his or her job a. because the company closed down or moved b. due to insufficient work c. because the position was abolished Do these probabilities add to \(1.0 ?\) If so, why?

What is meant by two mutually exclusive events? Give one example of two mutually exclusive events and another example of two events that are not mutually exclusive.

What is the complement of an event? What is the sum of the probabilities of two complementary events?