Exam 4: Introduction to Probability

As a company manager for Claimstat Corporation there is a 0.40 probability that you will be promoted this year. There is a 0.72 probability that you will get a promotion, a raise, or both. The probability of getting a promotion and a raise is 0.25. a. If you get a promotion, what is the probability that you will also get a raise? b. What is the probability that you will get a raise? c. Are getting a raise and being promoted independent events? Explain using probabilities. d. Are these two events mutually exclusive? Explain using probabilities.

An experiment consists of four outcomes with PE1) = 0.2, PE2) = 0.3, and PE3) = 0.4. The probability of outcome E4 is

Assume you have applied for two scholarships, a Merit scholarship M) and an Athletic scholarship A). The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3. a. What is the probability that you will receive a Merit scholarship? b. Are events A and M mutually exclusive? Why or why not? Explain. c. Are the two events A, and M, independent? Explain, using probabilities. d. What is the probability of receiving the Athletic scholarship given that you have been awarded the Merit scholarship? e. What is the probability of receiving the Merit scholarship given that you have been awarded the Athletic scholarship?

If X and Y are mutually exclusive events with PX) = 0.295, PY) = 0.32, then PX | Y) =

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

In a recent survey in a Statistics class, it was determined that only 60% of the students attend class on Fridays. From past data it was noted that 98% of those who went to class on Fridays pass the course, while only 20% of those who did not go to class on Fridays passed the course. a. What percentage of students is expected to pass the course? b. Given that a person passes the course, what is the probability that he/she attended classes on Fridays?

If A and B are mutually exclusive events with PA) = 0.4 and PB) = 0.5, then PA ∩ B) =

If A and B are mutually exclusive events with PA) = 0.8 and PB) = 0.6, then PA ∩ B) =

The probability assigned to each experimental outcome must be

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 in 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?

On a December day, the probability of snow is .30. The probability of a "cold" day is .50. The probability of snow and "cold" weather is .15. Are snow and "cold" weather independent events?

In a recent survey about appliance ownership, 58.3% of the respondents indicated that they own Maytag appliances, while 23.9% indicated they own both Maytag and GE appliances and 70.7% said they own at least one of the two appliances. Define the events as M = Owning a Maytag appliance G = Owning a GE appliance a. What is the probability that a respondent owns a GE appliance? b. Given that a respondent owns a Maytag appliance, what is the probability that the respondent also owns a GE appliance? c. Are events "M" and "G" mutually exclusive? Why or why not? Explain, using probabilities. d. Are the two events "M" and "G" independent? Explain, using probabilities.

The addition law is potentially helpful when we are interested in computing the probability of

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

In a random sample of UTC students 50% indicated they are business majors, 40% engineering majors, and 10% other majors. Of the business majors, 60% were females; whereas, 30% of engineering majors were females. Finally, 20% of the other majors were female. a. What percentage of students in this sample was female? b. Given that a person is female, what is the probability that she is an engineering major?

Assume your favorite football team has 3 games left to finish the season. The outcome of each game can be win, lose, or tie. How many possible outcomes exist?

If A and B are independent events with PA) = 0.4 and PB) = 0.6, then PA ∩ B) =

If A and B are mutually exclusive events with PA) = 0.4 and PB) = 0.45, then PA ∪ B) =

From a group of three finalists for a privately endowed scholarship, two individuals are to be selected for the first and second places. Determine the number of possible selections.

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