Exam 4: Introduction to Probability

In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.63, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465. a.What is the probability that UTC will defeat Furman given that they defeat Marshall? b.What is the probability that UTC will win at least one of the games? c.What is the probability of UTC winning both games? d.Are the outcomes of the games independent? Explain and substantiate your answer.

Given that event E has a probability of 0.31, the probability of the complement of event E

In statistical experiments, each time the experiment is repeated

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is not important is called

Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. In the past, 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the applicants. Assume events are independent of each other. a.What is the probability that you will be accepted to both universities? b.What is the probability that you will be accepted to at least one graduate program? c.What is the probability that one and only one of the universities will accept you? d.What is the probability that neither university will accept you?

A method of assigning probabilities based upon judgment is referred to as the

If a six sided die is tossed two times and "3" shows up both times, the probability of "3" on the third trial is

In a city, 60% of the residents live in houses and 40% of the residents live in apartments. Of the people who live in houses, 20% own their own business. Of the people who live in apartments, 10% own their own business. If a person owns his or her own business, find the probability that he or she lives in a house.

A student has to take 7 more courses before she can graduate. If none of the courses are prerequisites to others, how many groups of three courses can she select for the next semester?

Events A and B are mutually exclusive. Which of the following statements is also true?

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are possible?

Bayes' theorem is used to compute

The probability of an economic decline in the year 2008 is 0.23. There is a probability of 0.64 that we will elect a republican president in the year 2008. If we elect a republican president, there is a 0.35 probability of an economic decline. Let "D" represent the event of an economic decline, and "R" represent the event of election of a Republican president. a.Are "R" and "D" independent events? b.What is the probability of a Republican president and economic decline in the year 2008? c.If we experience an economic decline in the year 2008, what is the probability that there will a Republican president? d.What is the probability of economic decline or a Republican president in the year 2008? Hint: You want to find P(D $\cup$ R).

A very short quiz has one multiple choice question with five possible choices (a, b, c, d, e) and one true or false question. Assume you are taking the quiz but do not have any idea what the correct answer is to either question, but you mark an answer anyway. a.What is the probability that you have given the correct answer to both questions? b.What is the probability that only one of the two answers is correct? c.What is the probability that neither answer is correct? d.What is the probability that only your answer to the multiple choice question is correct? e.What is the probability that you have only answered the true or false question correctly?

The probability of the occurrence of event A in an experiment is 1/3. If the experiment is performed 2 times and event A did not occur, then on the third trial event A

From a group of six people, two individuals are to be selected at random. How many possible selections are possible?

Assume you are taking two courses this semester (A and B). The probability that you will pass course A is 0.835, the probability that you will pass both courses is 0.276. The probability that you will pass at least one of the courses is 0.981. a.What is the probability that you will pass course B? b.Is the passing of the two courses independent events? Use probability information to justify your answer. c.Are the events of passing the courses mutually exclusive? Explain.

From among 8 students how many committees consisting of 3 students can be selected?

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? (Note that each customer is either a purchaser or non-purchaser.)

An experiment consists of selecting a student body president, vice president, and a treasurer. All undergraduate students, freshmen through seniors, are eligible for the offices. How many sample points (possible outcomes as to the classifications) exist?