Probability theory provides the underlying mathematical foundation for assessing and analyzing situations involving uncertainty.

Probability theory provides the underlying mathematical foundation for assessing and analyzing situations involving uncertainty.

. As such, it is essential for thinking rationally and determining the course of action when future outcomes are not known with certainty.

For this week’s Exam, be sure to read “Appendix: Basic Principles of Probability Theory” in the Hastie and Dawes text. Then complete the multimedia piece, “Probability and Decision Making Activity.” This tutorial provides a brief introduction to probability theory, definitions of terms, and an explanation of how to calculate probabilities of events. After you complete the tutorial activity, you will take an exam based on the material from the Appendix and the tutorial.

First, solve the problems presented in the tutorial by responding as requested in the text boxes. As you move through the tutorial, feel free to consult the Hastie and Dawes Appendix or other texts.

After completing the tutorial, read and complete the exam problems in the “Week 3 Probability Problems Exam” handout. You are expected to do the exam without assistance from anyone other than your Instructor.

Hastie, R., & Dawes, R. M. (2010). Rational choice in an uncertain world (2nd ed.). Thousand Oaks, CA: Sage. “Appendix: Basic Principles of Probability Theory” (pp. 337–359)

Week 3 Probability Problems Exam

 

 

For problems 1–10, consider an experiment in which two dice are thrown simultaneously. If both dice do not have a clear upward facing side, the dice are thrown again. Each die has six faces, numbered 1–6. Assume that the dice are fair, each side is equally likely to occur, and the dice do not influence each other.

 

 

1. What is the probability that the sum of the upward facing sides of both dice is equal to two?

 

 

 

2. What is the probability that the sum of the upward facing sides of both dice is equal to three?

 

 

 

3. What is the probability that the sum of the upward facing sides of both dice is equal to seven?

 

 

 

4. What is the probability that the upward facing sides of the both dice are the same?

 

 

 

5. What is the probability that the upward facing sides of the both dice are different?

 

 

 

6. What is the probability that at least one of the upward facing sides of the dice is a four, five, or six?

 

 

 

7. What is the probability that exactly one of the upward facing sides of the dice is a four, five, or six?

 

 

 

8. What is the probability that neither of the upward facing sides of the dice are a four, five, or six?

 

 

 

9. After throwing the two dice, you observe that one of them is showing a six. What is the probability that the second die is also showing a six?

 

 

 

10. After throwing the two dice, you observe that one of them is showing a six. What is the probability that the second die is not showing a six?

 

 

 

Given the following probabilities, answer questions 11–25. Remember that  is called the complement of A, and P() = 1- P(A).

 

	A		Totals
B	0.18	0.45	0.63
	0.24	0.13	0.37
Totals	0.42	0.58	1.00

 

 

11. What is the P(A)?

 

 

 

12. What is the P(B)?

 

 

 

13. What is the P()?

 

 

 

14. What is the P(A and B)?

 

 

 

15. What is the P(A and B)?

 

 

 

16. What is the P(A and )?

 

 

 

17. What is the P(A|B)?

 

 

 

18. What is the P(|B)?

 

 

 

19. What is the P(B|A)?

 

 

 

 

 

20. What is P(A|)?

 

 

 

21. What is the P(A or B)?

 

 

 

22. What is the P(A or )?

 

 

 

23. What is the P(A and )?

 

 

 

24. Are A and independent of each other?

 

 

 

25. Are A and B independent of each other?

 

 

 

For problems 26–30, suppose P(A) = 0.54 and P(B|A) = 0.27 and P(B|) = 0.68.

 

26. What is P()?

 

 

27. What is P(A|B)?

 

 

28. What is P(A|)?

 

 

29. What is P(B)?

 

 

30. Is A independent of B?

 

 

 

For problems 31–35, suppose P(A) = 0.42 and P(B|A) = 0.34 and P(B|) = 0.34.

 

 

31. What is P()?

 

 

 

 

32. What is P(A| B)?

 

 

 

33. What is P(A|)?

 

 

 

34. What is P(B)?

 

 

 

35. Is A independent of B?

 

 

 

36. (Bonus Question) Suppose X is the amount of money a person earns in an hour where P(X = $5) =0.2, P(X =$10) = 0.1, P(X=$15) =0.5 and P(X=$20) = 0.2.

 

How much money would the person earn on average?

 

 

 

37. (Bonus Question) If the payoff of rolling two dice is the sum of the upper face of the two dice, what is the expected payoff of one roll of the two dice?

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