Markey's Casino

2. Markey's Casino

4. What is the probability of picking an ace?

5. Probability =

6. What is the probability of picking an ace? 4 / 52 = .077 or 7.7 chances in 100

7. Every card has the same probability of being picked

8. What is the probability of getting a 10, J, Q, or K?

9. (.077) + (.077) + (.077) + (.077) = .308 16 / 52 = .308

10. What is the probability of getting a 2 and then after replacing the card getting a 3 ?

11. (.077) * (.077) = .0059

12. What is the probability that the two cards you draw will be a black jack?

13. 10 Card = (.077) + (.077) + (.077) + (.077) = .308 Ace after one card is removed = 4/51 = .078 (.308)*(.078) = .024

14. Practice • What is the probability of rolling a “1” using a six sided dice? • What is the probability of rolling either a “1” or a “2” with a six sided dice? • What is the probability of rolling two “1’s” using two six sided dice?

15. Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? • What is the probability of rolling two “1’s” using two six sided dice?

16. Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? (.166) + (.166) = .332 • What is the probability of rolling two “1’s” using two six sided dice?

17. Practice • What is the probability of rolling a “1” using a six sided dice? 1 / 6 = .166 • What is the probability of rolling either a “1” or a “2” with a six sided dice? (.166) + (.166) = .332 • What is the probability of rolling two “1’s” using two six sided dice? (.166)(.166) = .028

18. Next step • Is it possible to apply probabilities to a normal distribution?

19. Theoretical Normal Curve -3 -2 -1 1 2  3 

20. Theoretical Normal Curve -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

21. We can use the theoretical normal distribution to determine the probability of an event. For example, do you know the probability of getting a Z score of 0 or less? .50 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

22. We can use the theoretical normal distribution to determine the probability of an event. For example, you know the probability of getting a Z score of 0 or less. .50 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

23. With the theoretical normal distribution we know the probabilities associated with every z score! The probability of getting a score between a 0 and a 1 is .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

24. What is the probability of getting a score of 1 or higher? .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

25. These values are given in Table C on page 384 .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

26. To use this table look for the Z score in column AColumn B is the area between that score and the mean Column B .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

27. To use this table look for the Z score in column AColumn C is the area beyond the Z score Column C .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

28. The curve is symmetrical -- so the answer for a positive Z score is the same for a negative Z score Column B Column C .3413 .3413 .1587 .1587 -3 -2 -1 1 2  3  Z-scores -3 -2 -1 0 1 2 3

29. Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? • Beyond z = 2.25? • Between the mean and z = -1.45

30. Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? • Between the mean and z = -1.45

31. Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? .0122 • Between the mean and z = -1.45

32. Practice • What proportion of the normal distribution is found in the following areas (hint: draw out the answer)? • Between mean and z = .56? .2123 • Beyond z = 2.25? .0122 • Between the mean and z = -1.45 .4265

33. Practice • What proportion of this class would have received an A on the last test if I gave A’s to anyone with a z score of 1.25 or higher? • .1056

35. Note • This is using a hypothetical distribution • Due to chance, empirical distributions are not always identical to theoretical distributions • If you sampled an infinite number of times they would be equal! • The theoretical curve represents the “best estimate” of how the events would actually occur

36. Theoretical Distribution

37. Empirical Distribution based on 52 draws

38. Empirical Distribution based on 52 draws

39. Empirical Distribution based on 52 draws

40. Theoretical Normal Curve 

41. Empirical Distribution

42. Empirical Distribution

43. Empirical Distribution

44. PROGRAM http://www.jcu.edu/math/isep/Quincunx/Quincunx.html

45. Theoretical Normal Curve  Normality frequently occurs in many situations of psychology, and other sciences