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10A Probability Revision - terminology

10A Probability Revision - terminology. 10A Probability Revision – Venn Diagrams. 10A Probability Revision - probability. 10A Probability Revision. Two fair dice are rolled simultaneously and the sum of the two numbers appearing uppermost is recorded as shown below.

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10A Probability Revision - terminology

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  1. 10A Probability Revision - terminology

  2. 10A Probability Revision – Venn Diagrams

  3. 10A Probability Revision - probability

  4. 10A Probability Revision • Two fair dice are rolled simultaneously and the sum of the two numbers appearing uppermost is recorded as shown below. • Find the probability that the sum will be: • a. 6 • (1,5) (2,4) (3,3) (4,2) (5,1)

  5. 10A Probability Revision • Two fair dice are rolled simultaneously and the sum of the two numbers appearing uppermost is recorded as shown below. • Find the probability that the sum will be: • b. 10 • (4,6) (5,5) (6,4)

  6. 10A Probability Revision • Two fair dice are rolled simultaneously and the sum of the two numbers appearing uppermost is recorded as shown below. • Find the probability that the sum will be: • c. a number less than 5 • (1,1) (1,2) (1,3) (2,1) (2,2) (3,1)

  7. 10A Probability Revision • Two fair dice are rolled simultaneously and the sum of the two numbers appearing uppermost is recorded as shown below. • Find the probability that the sum will be: • d. at least 9 • (3,6) (4,5) (4,6) (5,4) (5,5) (5,6) (6,3) (6,4) (6,5) (6,6)

  8. 10A Probability Revision • Two fair dice are rolled simultaneously and the sum of the two numbers appearing uppermost is recorded as shown below. • Find the probability that the sum will be: • e. an odd number.

  9. 10A Probability Revision • A bag contains 15 marbles, 5 black, 3 red, 4 blue, 2 white and 1 green. One marble is drawn randomly from the bag. • a. Determine the probability of each of the coloured marble being drawn • black red blue white green • Show that the probabilities sum to 1. • What is the probability that the marble drawn is: • not black? • either black or white? • neither blue nor green?

  10. 10A Probability Revision • A bag contains 15 marbles, 5 black, 3 red, 4 blue, 2 white and 1 green. One marble is drawn randomly from the bag. • a. Determine the probability of each of the coloured marble being drawn • black red blue white green • Show that the probabilities sum to 1. • What is the probability that the marble drawn is: • not black? • either black or white? • neither blue nor green? )

  11. 10A Probability Revision – the addition law of probability

  12. 10A Probability Revision – the addition law of probability a. If Pr(A) = 0.4, Pr(B) = 0.7 and Pr( A ∩ B) = 0.2 find Pr ( A  B) b. If Pr(A) = 0.6, Pr(B) = 0.8 and Pr ( A  B) = 0.9 find Pr( A ∩ B)

  13. 10A Probability Revision – the addition law of probability a. If Pr(A) = 0.4, Pr(B) = 0.7 and Pr( A ∩ B) = 0.2 find Pr ( A  B) b. If Pr(A) = 0.6, Pr(B) = 0.8 and Pr ( A  B) = 0.9 find Pr( A ∩ B)

  14. 10A Probability Revision – mutually exclusive events and independent events Mutually Exclusive Events Independent Events

  15. 10A Probability Revision mutually exclusive events and independent events Two fair dice are rolled with S representing the event of obtaining a number less than 4 on the first die and T representing the event of obtaining a number greater than 4 on the second die. Find: Pr(S) Pr(T) if events S and T are mutually exclusive if events S and T are independent. c. (1,5) (1,6) (2,5) (2,6) (3,5) (3,6) d.

  16. 10A Probability Revision mutually exclusive events and independent events Two fair dice are rolled with U representing the event of obtaining a 5 on the first die and V representing the event of the sum of the numbers on the two dice exceeding 10. Find: Pr(U) Pr(V) if events U and V are independent.

  17. 10A Probability Revision – Karnaugh Maps and probability tables.

  18. 10A Probability Revision – Karnaugh Maps and probability tables. For the probability table shown, A, is the events ‘not more than 17 years of age’ and B is the event ‘has a learner permit’. a. complete the probability table b. What do the following probabilities represent? i) ii) c. What is the probability that: a person over the age of 17 does not have a learner permit? a person has a learner permit and is older than 17? a person over the age of 17 has a learner permit or a person under the age of 17 does not have a learner permit? permit age

  19. 10A Probability Revision – conditional probability OR

  20. 10A Probability Revision conditional probability

  21. 10A Probability Revision conditional probability If Pr(A) = , Pr(B) = and Pr(A∩B) = find:

  22. 10A Probability Revision conditional probability If Pr(A) = , Pr(B) = and Pr(A∩B) = find: b. c.

  23. 10A Probability Revision conditional probability If Pr(A) = , Pr(B) = and Pr(A∩B) = find: d. if events A and B are mutually exclusive e. if events A and B are independent.

  24. 10A Probability Revision – Tree Diagrams • Nadia knows that if her car starts, she has an 80% • chance of getting to work on time. However, if her car • doesn’t start her chance of arriving on time is 50%. • If Nadia’s car starts 70% of the time what is the • probability that: • a. her car starts and she gets to work on time? 3

  25. 10A Probability Revision – Tree Diagrams Nadia knows that if her car starts, she has an 80% chance of getting to work on time. However, if her car doesn’t start her chance of arriving on time is 50%. If Nadia’s car starts 70% of the time what is the probability that: b. she arrives at work late? 3

  26. 10A Probability Revision – Tree Diagrams Nadia knows that if her car starts, she has an 80% chance of getting to work on time. However, if her car doesn’t start her chance of arriving on time is 50%. If Nadia’s car starts 70% of the time what is the probability that: c. she arrives at work on time? OR 3

  27. 10A Probability Revision – Tree Diagrams Nadia knows that if her car starts, she has an 80% chance of getting to work on time. However, if her car doesn’t start her chance of arriving on time is 50%. If Nadia’s car starts 70% of the time what is the probability that: d. her car starts given that she arrives on time? 3

  28. 10A Probability Revision – Tree Diagrams A fair coin is tossed three times. Find the probability of obtaining two heads given the first toss resulted in a tail. HHH, HHT, HTH, HTT, TTT, TTH, THT, THH

  29. 10A Probability Revision – Combinations nCr– from n different objects select r objects nCr = nCrcan be written as

  30. 10A Probability Revision – Combinations • A drawer contains 7 T-shirts, 3 are white and the rest are black. • If two T-shirts are randomly selected from the drawer simultaneously, find the probability that they are” • both black

  31. 10A Probability Revision – Combinations • A drawer contains 7 T-shirts, 3 are white and the rest are black. • If two T-shirts are randomly selected from the drawer simultaneously, find the probability that they are” • b. both white

  32. 10A Probability Revision – Combinations • A drawer contains 7 T-shirts, 3 are white and the rest are black. • If two T-shirts are randomly selected from the drawer simultaneously, find the probability that they are” • c. different colours

  33. 10A Probability Revision – Combinations A drawer contains 7 T-shirts, 3 are white and the rest are black. If two T-shirts are randomly selected from the drawer simultaneously, find the probability that they are” d. the same colour

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