Exam 4: Basic Probability Concepts

Consider the following events: A = The survey respondent is less than 40 years old. B = The survey respondent is 40 years or older. Events A and B are mutually exclusive and exhaustive.

Events are considered _________ if the occurrence of one is related to the probability of the occurrence of the other.

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

A survey of adults who typically work full time from home recorded their current education level.The results are shown in the table below. The probability that a randomly selected adult who works full time from home has a bachelor's degree or higher is ______.

In an experiment in which a coin is tossed twice,which of the following represents mutually exclusive and collectively exhaustive events?

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

A sample space contains _________________.

The complement of an event A,denoted by A^C,within the sample space S,is the event consisting of all outcomes of A that are not in S.

Peter applied to an accounting firm and a consulting firm.He knows that 30% of similarly qualified applicants receive job offers from the accounting firm,while only 20% of similarly qualified applicants receive job offers from the consulting firm.Assume that receiving an offer from one firm is independent of receiving an offer from the other.What is the probability that both firms offer Peter a job?

Suppose that 60% of the students do homework regularly.It is also known that 80% of students who had been doing homework regularly,end up doing well in the course.Only 20% of students who had not been doing homework regularly end up doing well in the course.Given that a student did well in the course,what is the probability that the student had been doing homework regularly?

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

There are three unfilled seats on a small plane,but 10 people showed up to try to get one of those three unfilled seats.If the airline picks three people at random to get on the plane,what is the probability you and your two kids will get on the plane?

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

If A and B are independent events,which of the following is correct?

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

As part of pharmaceutical testing for drowsiness as a side effect of a drug,200 patients are randomly assigned to one of two groups of 100 each.One group is given the actual drug and the other a placebo.The number of people who felt drowsy in the next hour is recorded as a.What is the probability that a randomly picked patient in the study feels drowsy in the next hour? b.What is the probability that a randomly picked patient in the study takes the placebo or feels drowsy in the next hour? c.Given that the patient was given the drug,what is the probability that he or she feels drowsy in the next hour? d.Is whether a patient feels drowsy independent of taking the drug? Explain using probabilities.

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

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.

Suppose that 60% of the students do homework regularly.It is also known that 80% of students who had been doing homework regularly end up doing well in the course.Only 20% of students who had not been doing homework regularly end up doing well in the course.What is the probability that a student does well in the course?

The likelihood of Company A's stock price rising is 20%,and the likelihood of Company B's stock price rising is 30%.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 ______.