Exam 4: Basic Probability Concepts

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.

Let ,and ,and .Compute .

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. What is the probability the earnings announcement is below the forecast?

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)___________.

The odds for encountering rain on a 500-mile car trip are three to one.What is the probability of rain on this trip?

What is a simple event?

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 thinks that with the appropriate preparation,she has a 70% chance of getting an A in Marketing.She also believes 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.

Mutually exclusive and collectively exhaustive events ______________.

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. The probability that a respondent is at least 30 years old is the closest to ______.

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?

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.

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

An intuitive way to express the total probability rule is with the help of a _______________.

A(n)________ probability is calculated as the relative frequency with which an event occurs.

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. The probability that a respondent read a book in the last month and is at least 30 years old is the closest to _______.

There are 30 Major League Baseball teams in the National League.Five of these teams will make the playoffs at the end of the season.The number of unique groups of teams that can make the playoffs is ______.

An experiment consists of rolling a fair die.Find the probability that we roll a 4 or a 6.

There are 23 chess players participating in a weekend tournament.Prices are awarded to the first-,second-,third-,and fourth-place finishers.The number of different ways these four places can be filled by those playing is ______.

The probability of a union of events can be greater than 1.

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 to the survey is male is the closest to ____.