Exam 4: Introduction to Probability

A survey of adults who typically work full time from home recorded their current education level. The results are shown in the table below. Calculating the probability that a randomly selected adult who works full time from home has an associate degree is using ________ probability.

Exams are approaching and Helen is allocating time to studying for exams. She feels that with the appropriate amount of studying, she has an 80% chance of getting an A in Marketing. She also feels that she has a 60% chance of getting an A in Spanish with the appropriate amount of studying. Given the demands on her time, she feels that she has only a 45% chance of getting an A in both classes. What is the probability that Helen does not get an A in either class?

An analyst believes the probability that U.S. stock returns exceed long-term corporate bond returns over a five-year period is based on personal assessment. This type of probability is best characterized as a(n) ________.

Mark Zuckerberg, the founder of Facebook, announced that he will eat meat only from animals that he has killed himself (Vanity Fair, November 2011). Suppose 257 people were asked, "Does the idea of killing your own food appeal to you, or not?" The accompanying contingency table, cross-classified by gender, is produced from the 187 respondents. The probability that a respondent is male and feels that the idea of killing his own food is appealing is the closest to ________.

In January of 2012, the second stop for a Republican to get votes toward the presidential nomination was at the New Hampshire Primary. The following exhibit shows the votes several candidates received from registered Republicans and Independents. Source: ABC News If a randomly selected voter voted for Jon Huntsman, what is the probability he or she is a Republican?

The following table summarizes the ages of the 400 richest Americans. Suppose we select one of these individuals. Find the probability that the selected individual is less than 80 years old.

At a local bar in a small town, beer and wine are the only two alcoholic options. The manager noted that of all male customers, 150 ordered beer, 40 ordered wine, and 20 asked for soft drinks. Of female customers 38 ordered beer, 20 ordered wine, and 12 asked for soft drinks. What is the probability that a randomly selected customer orders wine?

The union of events A and B, denoted by A ∪ B, ________.

Exams are approaching and Helen is allocating time to studying for exams. She plays for the very successful women's lacrosse team and must schedule her studying around lacrosse practices and play-off games. The entire team assumes that the probability of making the play-offs is 50%. Helen thinks that with the appropriate preparation, she has a 70% chance of getting an A in Marketing, but this chance decreases to 60% if the lacrosse team makes the play-offs. Find the probability of getting an A in Marketing and making the lacrosse play-offs.

Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. Given that a respondent read a book in the last month, the probability that he or she is at least 30 years old is the closest to ________.

When some objects are randomly selected, which of the following is true?

For the sample space S = {apple pie, cherry pie, peach pie, pumpkin pie}, what is the complement of A = {pumpkin pie, cherry pie}?

Let P(A ∩B) = 0.3, and P(A ∩ B^c) = 0.15. Compute P(B|A).

How many ways can a potential four-letter word, whether or not it has a meaning, be created out of 10 available different letters?

A certain weightlifter is prone to back injury. He finds that he has a 20% chance of hurting his back if he uses the proper form of bending at the hips and keeping his spine locked. The probability that he will hurt his back with bad form is 95%. The probability that he uses proper form is 75%. What is the probability he hurts his back?

If A and B are ________ ________ events, then the addition rule is defined as P(A ∪B) = P(A) + P(B).

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35, and those 35 years of age or older. Find the probability that an individual prefers biking given that he or she is 35 years old or older.

Approximately 70% of the state of Pennsylvania sits on a shale formation from which natural gas may be extracted. If a geological test is positive, it has an 80% accuracy rate in correctly identifying a productive drilling site (shale is under the ground). If there is no shale under the ground, geological testing is falsely positive with a probability of 20%. Suppose the result of the geological test comes back positive (the test says there is shale under the ground). It is most important for us to know the probability that there is indeed shale under the ground given a positive geological test result. Find this probability.

Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and fund B will rise in price?

Bayes' theorem is a rule that uses the total probability rule and the addition rule to update the probability of the event.