Exam 4: Basic Probability Concepts

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.

An analyst has a limit order outstanding on a stock.He argues that the probability that the order will execute before the close of trading is 0.20.Thus,the odds for the order executing before the close of trading are ________.

Subjective probability is assigned to an event by drawing on logical analysis.

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 that a randomly selected customer prefers vanilla?

Boeing currently produces five models of airplanes for commercial sale.The airline that Lauren works for is rapidly expanding and would like to purchase three airplanes of different models to service various routes.Her job is to analyze which three to buy.How many combinations will she have to analyze?

Based on his batting average,a baseball player has a 32.7% chance of hitting the ball on his next at-bat.Find the odds against this player getting a hit.

Exhibit 4-4.An investor is keeping a careful eye on the real estate markets in Las Vegas and the Inland Empire.The following are her predictions for the real estate market in 2012. • With 0.32 probability,foreclosures will increase in Las Vegas. • With 0.46 probability,foreclosures will increase in Las Vegas or the Inland Empire. • With 0.27 probability,foreclosures will increase in Las Vegas and the Inland Empire. Refer to Exhibit 4-4.What is the probability that foreclosures will increase in the Inland Empire given that they increased in Vegas?

An analyst expects that 20 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 90% chance that this ratio will be negative.If the company is not headed for a decline,there is only a 10% chance that the ratio will be negative.The analyst randomly selects a company with a negative ratio.Based on Bayes' theorem,the posterior probability that the company will experience a decline is ____.

The likelihood of Company A's stock price rising is 20 percent,and the likelihood of Company B's stock price rising is 30 percent.Assume that the returns of Company A and Company B stock are independent of each other.The probability that the stock price of at least one of the companies will rise is _______.

Which of the following are mutually exclusive events of an experiment in which two coins are tossed?

Exhibit 4-4.An investor is keeping a careful eye on the real estate markets in Las Vegas and the Inland Empire.The following are her predictions for the real estate market in 2012. • With 0.32 probability,foreclosures will increase in Las Vegas. • With 0.46 probability,foreclosures will increase in Las Vegas or the Inland Empire. • With 0.27 probability,foreclosures will increase in Las Vegas and the Inland Empire. Refer to Exhibit 4-4.What is the probability that foreclosures will increase in the Inland Empire?

For two independent events A and B,the probability of their intersection is zero.

Exhibit 4-6.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 Refer to Exhibit 4-6.If a randomly selected voter voted for Jon Huntsman,what is the probability he is a Republican?

Let ,and .Calculate .

A certain state wants to use three letters followed by three digits on their license plates.If each letter and each digit can only be used once,how many possible license plates can be created?

A probability based on logical analysis rather than on observation or personal judgment is best referred to as a(n)_______________.

How many ways can a potential 4-letter word,whether or not it has a meaning,be created out of 10 available different letters?

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 analyst issued a good report given Apple's earnings announcement was below the forecast?

The odds for encountering rain on a 500-mile car trip are 3 to 1.What is the probability of rain on this trip?

How many project teams composed of 5 students can be created out of a class of 10 students?