Exam 4: Basic Probability Concepts

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.She feels that with the appropriate preparation,she has a 70% chance of getting an A in Marketing.She also feels that this chance will decrease to 60% if the lacrosse team makes the play-offs.Are getting an A on the exam and being in the lacrosse play-offs independent events? Show evidence of your response.

An analyst expects that 10 percent of all publicly traded companies will experience a decline in earnings next year.The analyst has developed a ratio to help forecast this decline.If the company is headed for a decline,there is a 70% chance that this ratio will be negative.If the company is not headed for a decline,there is only a 20% chance that the ratio will be negative.The analyst randomly selects a company and its ratio is negative.Based on Bayes' theorem,the posterior probability that the company will experience a decline is ____.

Exhibit 4-3.The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla,chocolate,or swirled frozen yogurt.The results are displayed next. Refer to Exhibit 4-3.What is the probability a randomly selected customer prefers chocolate given he or she is at least 25 years old?

For an experiment in which a single die is rolled,the sample space is __________.

Exhibit 4-5.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. Refer to Exhibit 4-5.Compute the probability that an individual is under 35 and prefers running.

Exhibit 4-1.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. Refer to Exhibit 4-1.Given that a respondent read a book in the last month,the probability that he/she is at least 30 years old is closest to ________.

After extensive research,an analyst asserts that there is an 80% chance that ABC Corporation will beat its EPS forecast.Analogously,the odds for the company beating its EPS forecast are _______.

Events are exhaustive if they do not share common outcomes of a sample space.

Find the missing values marked xx and yy in the following contingency table:

An experiment consists of tossing three fair coins.What is the probability of tossing two tails?

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

Which of the following is not an event when considering the sample space of tossing two coins?

The odds against winning $1.00 in the lottery are 19 to 1.What is the probability of winning $1.00 in the lottery?

Combinations are used when the order in which different objects are arranged matters.

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.

Two stocks,A and B,have a historical correlation indistinguishable from zero.The probability that stock A increases next year is 0.2,and the probability that stock B increases next year is 0.4.Calculate the probability that A and B both increase next year.

Members of the saxophone section of a marching band are asked to attend saxophone-only practices once a week.These practices are not mandatory,but they are the only opportunity for the entire section to play together in preparation for the marching season.The section leader has noted that 70% of the section regularly attends practices.Further,given that they attend regularly,there is a 40% chance of earning an A on their performance when later graded by the band director.If they do not attend regularly,there is only a 10% chance of earning an A on their performance.What is the probability that a randomly chosen musician receives an A on their performance?

Exhibit 4-7.An investor in Apple is worried the latest management earnings forecast is too aggressive and the company will fall short.His favorite analyst that covers Apple is going to release his report on Apple the week before the earnings announcement.Report stands for the analyst's report,and Forecast stands for the earnings announcement. Refer to Exhibit 4-7.What is the probability the earnings announcement is below the forecast?

Which of the following represents a subjective probability?

The total probability rule is useful only when the unconditional probability is expressed in terms of probabilities conditional on two mutually exclusive and exhaustive events.