Probability Definitions
Probability Definitions Probability: the chance of something happening
Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes
Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely ...
Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely ...
Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely ...
Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely ...
Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely ...
Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely ...
Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely ...
Probability Theory
Probability Theory
Probability Theory P(E)=0: E never happens
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is ...
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is ...
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is ...
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is ...
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is ...
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is ...
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is ...
Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is ...
Complementary Events
Complementary Events
Complementary Events e.g. What is the probability of totaling at least 3?
Complementary Events e.g. What is the probability of totaling at least 3?
Complementary Events e.g. What is the probability of totaling at least 3?
Complementary Events e.g. What is the probability of totaling at least 3?
Non-Mutually Exclusive Events
Non-Mutually Exclusive Events
Non-Mutually Exclusive Events e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
Non-Mutually Exclusive Events e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
Non-Mutually Exclusive Events e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
Non-Mutually Exclusive Events e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5.  The score for each turn is calcu...
(iii) What is the probability that the sum of the scores in the first  two turns is less than 45?
(iii) What is the probability that the sum of the scores in the first  two turns is less than 45?
(iii) What is the probability that the sum of the scores in the first  two turns is less than 45?
(iii) What is the probability that the sum of the scores in the first  two turns is less than 45?
(iii) What is the probability that the sum of the scores in the first  two turns is less than 45?
(iii) What is the probability that the sum of the scores in the first  two turns is less than 45? Exercise 10A; odd Exerci...
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12X1 T09 01 definitions & theory

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12X1 T09 01 definitions & theory

  1. 1. Probability Definitions
  2. 2. Probability Definitions Probability: the chance of something happening
  3. 3. Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes
  4. 4. Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely Events: events which have an equal chance of happening
  5. 5. Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely Events: events which have an equal chance of happening Mutually Exclusive Events: only one possible outcome can occur at any one time.
  6. 6. Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely Events: events which have an equal chance of happening Mutually Exclusive Events: only one possible outcome can occur at any one time. e.g. a coin can be either a head or a tail, not both
  7. 7. Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely Events: events which have an equal chance of happening Mutually Exclusive Events: only one possible outcome can occur at any one time. e.g. a coin can be either a head or a tail, not both Non-Mutually Exclusive Events: more than one outcome could possibly happen at any one time
  8. 8. Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely Events: events which have an equal chance of happening Mutually Exclusive Events: only one possible outcome can occur at any one time. e.g. a coin can be either a head or a tail, not both Non-Mutually Exclusive Events: more than one outcome could possibly happen at any one time e.g. a number could be both even and a multiple of three
  9. 9. Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely Events: events which have an equal chance of happening Mutually Exclusive Events: only one possible outcome can occur at any one time. e.g. a coin can be either a head or a tail, not both Non-Mutually Exclusive Events: more than one outcome could possibly happen at any one time e.g. a number could be both even and a multiple of three
  10. 10. Probability Definitions Probability: the chance of something happening Sample Space: all possible outcomes Equally Likely Events: events which have an equal chance of happening Mutually Exclusive Events: only one possible outcome can occur at any one time. e.g. a coin can be either a head or a tail, not both Non-Mutually Exclusive Events: more than one outcome could possibly happen at any one time e.g. a number could be both even and a multiple of three
  11. 11. Probability Theory
  12. 12. Probability Theory
  13. 13. Probability Theory P(E)=0: E never happens
  14. 14. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen
  15. 15. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen
  16. 16. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen
  17. 17. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen
  18. 18. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is the probability that they; ( i ) total 3? ( ii ) total 7?
  19. 19. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is the probability that they; ( i ) total 3? ( ii ) total 7? 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6
  20. 20. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is the probability that they; ( i ) total 3? ( ii ) total 7? 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6
  21. 21. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is the probability that they; ( i ) total 3? ( ii ) total 7? 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6
  22. 22. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is the probability that they; ( i ) total 3? ( ii ) total 7? 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6
  23. 23. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is the probability that they; ( i ) total 3? ( ii ) total 7? 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6
  24. 24. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is the probability that they; ( i ) total 3? ( ii ) total 7? 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6
  25. 25. Probability Theory P(E)=0: E never happens P(E)=1: a certain event. E must happen e.g. A pair of dice are thrown. What is the probability that they; ( i ) total 3? ( ii ) total 7? 1 1 1 2 1 3 1 4 1 5 1 6 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6
  26. 26. Complementary Events
  27. 27. Complementary Events
  28. 28. Complementary Events e.g. What is the probability of totaling at least 3?
  29. 29. Complementary Events e.g. What is the probability of totaling at least 3?
  30. 30. Complementary Events e.g. What is the probability of totaling at least 3?
  31. 31. Complementary Events e.g. What is the probability of totaling at least 3?
  32. 32. Non-Mutually Exclusive Events
  33. 33. Non-Mutually Exclusive Events
  34. 34. Non-Mutually Exclusive Events e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
  35. 35. Non-Mutually Exclusive Events e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
  36. 36. Non-Mutually Exclusive Events e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
  37. 37. Non-Mutually Exclusive Events e.g. What is the chance of picking an Ace or a heart from a regular deck of playing cards?
  38. 38. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c)
  39. 39. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c) 0 X 0 = 0 0 X 1 = 0 0 X 2 = 0 0 X 3 = 0 0 X 4 = 0 0 X 5 = 0 1 X 0 = 0 1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 1 X 4 = 4 1 X 5 = 5 2 X 0 = 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 3 X 0 = 0 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 4 X 0 = 0 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 5 X 0 = 0 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25
  40. 40. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c) (i) What is the probability of scoring zero on the first turn? 0 X 0 = 0 0 X 1 = 0 0 X 2 = 0 0 X 3 = 0 0 X 4 = 0 0 X 5 = 0 1 X 0 = 0 1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 1 X 4 = 4 1 X 5 = 5 2 X 0 = 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 3 X 0 = 0 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 4 X 0 = 0 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 5 X 0 = 0 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25
  41. 41. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c) 0 X 0 = 0 0 X 1 = 0 0 X 2 = 0 0 X 3 = 0 0 X 4 = 0 0 X 5 = 0 1 X 0 = 0 1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 1 X 4 = 4 1 X 5 = 5 2 X 0 = 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 3 X 0 = 0 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 4 X 0 = 0 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 5 X 0 = 0 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25 (i) What is the probability of scoring zero on the first turn?
  42. 42. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c) 0 X 0 = 0 0 X 1 = 0 0 X 2 = 0 0 X 3 = 0 0 X 4 = 0 0 X 5 = 0 1 X 0 = 0 1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 1 X 4 = 4 1 X 5 = 5 2 X 0 = 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 3 X 0 = 0 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 4 X 0 = 0 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 5 X 0 = 0 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25 (i) What is the probability of scoring zero on the first turn?
  43. 43. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c) 0 X 0 = 0 0 X 1 = 0 0 X 2 = 0 0 X 3 = 0 0 X 4 = 0 0 X 5 = 0 1 X 0 = 0 1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 1 X 4 = 4 1 X 5 = 5 2 X 0 = 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 3 X 0 = 0 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 4 X 0 = 0 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 5 X 0 = 0 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25 (i) What is the probability of scoring zero on the first turn? (ii) What is the probability of scoring 16 or more on the first turn?
  44. 44. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c) 0 X 0 = 0 0 X 1 = 0 0 X 2 = 0 0 X 3 = 0 0 X 4 = 0 0 X 5 = 0 1 X 0 = 0 1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 1 X 4 = 4 1 X 5 = 5 2 X 0 = 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 3 X 0 = 0 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 4 X 0 = 0 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 5 X 0 = 0 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25 (i) What is the probability of scoring zero on the first turn? (ii) What is the probability of scoring 16 or more on the first turn?
  45. 45. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c) 0 X 0 = 0 0 X 1 = 0 0 X 2 = 0 0 X 3 = 0 0 X 4 = 0 0 X 5 = 0 1 X 0 = 0 1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 1 X 4 = 4 1 X 5 = 5 2 X 0 = 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 3 X 0 = 0 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 4 X 0 = 0 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 5 X 0 = 0 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25 (i) What is the probability of scoring zero on the first turn? (ii) What is the probability of scoring 16 or more on the first turn?
  46. 46. In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice. 2004 Mathematics HSC Q6c) 0 X 0 = 0 0 X 1 = 0 0 X 2 = 0 0 X 3 = 0 0 X 4 = 0 0 X 5 = 0 1 X 0 = 0 1 X 1 = 1 1 X 2 = 2 1 X 3 = 3 1 X 4 = 4 1 X 5 = 5 2 X 0 = 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 3 X 0 = 0 3 X 1 = 3 3 X 2 = 6 3 X 3 = 9 3 X 4 = 12 3 X 5 = 15 4 X 0 = 0 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 5 X 0 = 0 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25 (i) What is the probability of scoring zero on the first turn? (ii) What is the probability of scoring 16 or more on the first turn?
  47. 47. (iii) What is the probability that the sum of the scores in the first two turns is less than 45?
  48. 48. (iii) What is the probability that the sum of the scores in the first two turns is less than 45?
  49. 49. (iii) What is the probability that the sum of the scores in the first two turns is less than 45?
  50. 50. (iii) What is the probability that the sum of the scores in the first two turns is less than 45?
  51. 51. (iii) What is the probability that the sum of the scores in the first two turns is less than 45?
  52. 52. (iii) What is the probability that the sum of the scores in the first two turns is less than 45? Exercise 10A; odd Exercise 10B; odd Exercise 10C; odd (not 23)

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