Exam 4: Introduction to Probability

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?

Mutually exclusive events ________.

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?

Let P(A) = 0.6, P(B) = 0.5, and P((A ∪ B)^c) = 0.1. Calculate P(A | B).

The following probability table shows probabilities concerning Favorite Subject and Gender. What is the probability of selecting an individual preferring science if she is female?

The intersection of events A and B, denoted by A ∩ B, ________.

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.

How many ways can a committee of four students be selected from a 15-member club?

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 2016. • 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. What is the probability that foreclosures will increase in the Inland Empire?

In January 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 What is the probability that a randomly selected voter voted for Ron Paul?

A company is bidding on two projects, A and B. The probability that the company wins project A is 0.40 and the probability that the company wins project B is 0.25. Winning project A and winning project B are independent events. What is the probability that the company wins project A or project B?

Let P(B|A) = P(B). Suppose A and B are independent. What is the value of P(B|A)?

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

5! is equal to ________.

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. Convert the contingency table to a joint probability table.

A pension plan gives you 12 possible funds in which to invest, but you are allowed to hold four at any given point in time. How many possible combinations of the 12 funds could you have in your portfolio?

Joint probability of two independent events A and B equals the sum of the individual probabilities of A and B.

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

Let A and B be two independent events with P(A) = 0.40 and P(B) = 0.20. Which of the following is correct?

The union of events A = {apple pie, peach pie, pumpkin pie} and B = {cherry pie, blueberry pie, pumpkin pie} is ________.