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Effective Probability Calculations with Fundamental Principles

Discover how to use combinations, permutations, and geometric probability in various scenarios with this comprehensive lesson. Learn to count outcomes and apply fundamental counting principles to solve probability problems efficiently.

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Effective Probability Calculations with Fundamental Principles

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  1. Use lists, tables and tree diagrams to represent sample spaces • I can use the Fundamental counting Principle to count outcomes Lesson 12.1

  2. experiment outcomes outcome trial event experiment sample space tree diagram

  3. H H T T T H H T H T H H H H H H T H H H T T T T T T H T H H T T T T

  4. H T 1 H1 T1 H 1 H 2 H 3 H 4 H 5 H 6 T 1 T 2 T 3 T 4 T 5 T 6 2 H2 T2 3 H3 T3 4 H4 T4 5 H5 T5 6 H6 T6

  5. kids with cheese and pickles P C NP K P NC NP 12 different orders possible P C R NP NC P 3 ⦁ 2 ⦁ 2 = 12 NP P C D NP NC P NP

  6. N1 ⦁ N2 ⦁ N3 ⦁ …..

  7. 960,000 10 ⦁ 2 ⦁ 12 ⦁ 5 ⦁ 20 ⦁ 20 ⦁ 2 =

  8. 83,160 11 ⦁ 7 ⦁ 5 ⦁ 3 ⦁ 6 ⦁ 4 ⦁ 3 =

  9. ASSIGNMENT 12-1 worksheet

  10. I can use permutations with probability • I can use combinations with probability Lesson 12.2

  11. n! 4 ⦁ 3 ⦁ 2 ⦁ 1 = 24 = 3,628,800 • 10 ⦁ 9 ⦁ 8 ⦁ 7⦁ 6 ⦁ 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 10! = • 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 = 120 5! =

  12. order n Pr n! (n – r)! 5! • 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 5 P2 = = 20 = • 3 ⦁ 2 ⦁ 1 (5 – 2)! 6! • 6 ⦁ 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 6 P4 = = 360 = • 2 ⦁ 1 (6 – 4)!

  13. 10 P4 = 5040 8 P3 = 336

  14. order n! n Cr r!(n – r)! • 10 ⦁ 9 ⦁ 8 ⦁ 7 ⦁ 6 ⦁ 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 10! 10 C4 = = • 4 ⦁ 3 ⦁ 2 ⦁ 1 • ⦁ 6 ⦁ 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 4! (10 – 4)! 5040 = 210 24

  15. 5! • 5 ⦁ 4 ⦁ 3 ⦁ 2 ⦁ 1 5 C 2 = = 2! (5 – 2)! • 2 ⦁ 1 • ⦁ 3 ⦁ 2 ⦁ 1 20 = 10 2

  16. 336 8 P3 = 10 5 C3 = 60 C 5 = 5,461,512 4845 20 C4 = 24 4 P4 =

  17. 1 1 = 20 C 6 38,760 1 1 = 380 20 P 2

  18. 1 1 = 65,780 26 C 5 1 1 = 870 30 P 2

  19. ASSIGNMENT 12-2 worksheet

  20. I can solve problems involving geometric probability • I can solve problems involving sectors and segments of circles Lesson 12.3

  21. chance Area of B Total area

  22. Area of square 4 = = 0.14 Total area 28

  23. Area of shaded 48 = = 0.48 Total area 100

  24. 80 P(red) = 360 = 0.222

  25. 120 P(blue) = 360 = 0.333

  26. π(22) = 4π – π(12) = 1π = 3π (area of white region) π(32) = 9π (area of target) 3π P(white) = = 0.333 9π

  27. π(62) = 36π – π(32) = 9π = 27π (area of blue region) π(62) = 36π (area of target) 27π P(blue) = = 0.75 36π

  28. ASSIGNMENT 12-3 worksheet

  29. I can find the probabilities of independent and dependent events • I can find the probability of events given the occurrence of other events Lesson 12.4

  30. 2 or more does not affects

  31. independent dependent independent

  32. independent dependent

  33. P(A and B) = P(A) ⦁ P(B) 1 1 1 1 1 36 6 6 6 6 ⦁ =

  34. 1 1 1 1 1 3 3 3 3 9 ⦁ =

  35. P(A and B) = P(A) ⦁ P(B | A)

  36. P(regular 1st and 2nd) ⦁ = 8 7 56 156 13 12

  37. ⦁ = ⦁ = 6 30 5 3 1 3 90 90 10 10 9 9 TV TV TV TV TV TV C V V V

  38. ASSIGNMENT 12-4 worksheet

  39. I can find the probabilities of events using two-way frequency tables Lesson 12.5

  40. 20 10 12 18 30 P(male) = 20/30 P(female) = 10/30 P(11th) = 12/30 P(12th) = 18/30

  41. 20 10 12 18 30 4/12 6/10 12/18 0

  42. 44 25 69 91 59 32 84 160 76 69 76

  43. 43.1% 15.6% 56.9% 20% 36.9% 100% 47.5% 52.5% 47.5% of 285 0.475(285) ≈ 135 students ≈ 0.579 44/76

  44. ASSIGNMENT 12-5 worksheet

  45. I can find probabilities of events that are mutually exclusive and events that are not mutually exclusive Lesson 12.6

  46. mutually exclusive yes no no

  47. no no no yes

  48. P(A or B) = P(A) + P(B) 22 10 12 + = 35 35 35 35

  49. + = 41 10 15 4 16 10 6 36 80 36 80 80 80 36 + + =

  50. P(A or B) = P(A) + P(B) – P(A and B) P(H or K) = –P(H and K) P(H) + P(K) 16 13 1 4 + – = 52 52 52 52

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