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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
    4 主题
  3. Histograms Aqa Higher
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  4. Statistical-Diagrams Aqa Higher
    5 主题
  5. Averages-Ranges-And-Data Aqa Higher
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  6. Combined-And-Conditional-Probability Aqa Higher
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  7. Tree-Diagrams Aqa Higher
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  8. Simple-Probability-Diagrams Aqa Higher
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  9. Transformations Aqa Higher
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  10. Vectors Aqa Higher
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  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
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  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
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  13. Pythagoras-And-Trigonometry Aqa Higher
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  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
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  15. Congruence-Similarity-And-Geometrical-Proof Aqa Higher
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  16. Volume-And-Surface-Area Aqa Higher
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  17. Circles-Arcs-And-Sectors Aqa Higher
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  18. Area-And-Perimeter Aqa Higher
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  19. Circle-Theorems Aqa Higher
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  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
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  21. Angles-In-Polygons-And-Parallel-Lines Aqa Higher
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  22. Symmetry-And-Shapes Aqa Higher
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  23. Exchange-Rates-And-Best-Buys Aqa Higher
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  24. Standard-And-Compound-Units Aqa Higher
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  25. Direct-And-Inverse-Proportion Aqa Higher
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  26. Problem-Solving-With-Ratios Aqa Higher
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  27. Ratios Aqa Higher
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  28. Sequences Aqa Higher
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  29. Transformations-Of-Graphs Aqa Higher
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  30. Graphing-Inequalities Aqa Higher
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  31. Solving-Inequalities Aqa Higher
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  32. Real-Life-Graphs Aqa Higher
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  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
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  34. Equation-Of-A-Circle Aqa Higher
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  35. Functions Aqa Higher
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  36. Forming-And-Solving-Equations Aqa Higher
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  37. Graphs-Of-Functions Aqa Higher
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  38. Linear-Graphs Aqa Higher
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  39. Coordinate-Geometry Aqa Higher
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  40. Iteration Aqa Higher
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  41. Simultaneous-Equations Aqa Higher
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  42. Quadratic-Equations Aqa Higher
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  43. Linear-Equations Aqa Higher
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  44. Algebraic-Proof Aqa Higher
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  45. Rearranging-Formulas Aqa Higher
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  46. Algebraic-Fractions Aqa Higher
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  47. Completing-The-Square Aqa Higher
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  48. Factorising Aqa Higher
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  49. Expanding-Brackets Aqa Higher
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  50. Algebraic-Roots-And-Indices Aqa Higher
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  51. Using-A-Calculator Aqa Higher
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  52. Surds Aqa Higher
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  53. Rounding-Estimation-And-Bounds Aqa Higher
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  54. Fractions-Decimals-And-Percentages Aqa Higher
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  55. Introduction Aqa Higher
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  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
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  57. Percentages Aqa Higher
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  58. Fractions Aqa Higher
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  59. Powers-Roots-And-Standard-Form Aqa Higher
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  60. Prime-Factors-Hcf-And-Lcm Aqa Higher
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  61. Number-Operations Aqa Higher
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Exam code:8300

Combined probability

How do I calculate combined probabilities?

  • You can calculate probabilities of one event after another without needing tree diagrams

    • These are called combined (or successive) probabilities

  • There are two rules to learn

    • And means multiply and or means add

    • P(A and B) = P(A) x P(B)

    • P(AA or BB) = P(AA) + P(BB)

  • Try to rephrase each question using and / or

    • For example, when flipping a coin twice: 

      • P(two heads) = P(head and head)

      • P(both the same) = P(head and head or tail and tail) = P(HH) + P(TT)

  • Remember that P(not A) = 1 – P(A)

What does independent mean?

  • Independent events are events that do not affect each other

    • e.g. the probability of rolling a 6 on a fair dice and the probability of getting a head when flipping a coin

  • Be careful: questions ‘without replacement’ are not independent

    • e.g. the probability of taking a red card out of a pack, not replacing it, then finding the probability of taking a second red card out of the same pack

      • The first event affected the number of cards left for the second event

Worked Example

A box contains 3 blue counters and 8 red counters.
A counter is taken at random and its colour is noted.
The counter is put back into the box.
A second counter is then taken at random, and its colour is noted.

Work out the probability that

(a) both counters are red,

P(both red) = P(red and red) 
This is P(red) × P(red) using the ‘and rule’

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 8 over 11 cross times 8 over 11 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell bold 64 over bold 121 end cell end table

(b) the two counters are of different colours.

P(different colours) = P(blue and red or red and blue)
This is P(B and R) + P(R and B) using the ‘or rule’
This is P(B) × P(R) + P(R) × P(B) using the ‘and rule’ twice

table row blank blank cell 8 over 11 cross times 3 over 11 plus 3 over 11 cross times 8 over 11 end cell row blank equals cell 24 over 121 plus 24 over 121 end cell end table

table row blank blank cell bold 48 over bold 121 end cell end table

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