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Maths Gcse Wjec-Eduqas Higher

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  1. Scatter-Graphs-And-Correlation Wjec-Eduqas Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Wjec-Eduqas Higher
    4 主题
  3. Histograms Wjec-Eduqas Higher
    3 主题
  4. Statistical-Diagrams- Wjec-Eduqas Higher
    6 主题
  5. Averages-Ranges-And-Data Wjec-Eduqas Higher
    8 主题
  6. Combined-And-Conditional-Probability Wjec-Eduqas Higher
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  7. Tree-Diagrams- Wjec-Eduqas Higher
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  8. Simple-Probability-Diagrams- Wjec-Eduqas Higher
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  9. Introduction-To-Probability Wjec-Eduqas Higher
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  10. Transformations Wjec-Eduqas Higher
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  11. Vectors Wjec-Eduqas Higher
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  12. 3D-Pythagoras-And-Trigonometry Wjec-Eduqas Higher
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  13. Sine-Cosine-Rule-And-Area-Of-Triangles- Wjec-Eduqas Higher
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  14. Pythagoras-And-Trigonometry Wjec-Eduqas Higher
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  15. Area-And-Volume-Of-Similar-Shapes Wjec-Eduqas Higher
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  16. Congruence-Similarity-And-Geometrical-Proof Wjec-Eduqas Higher
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  17. Volume-And-Surface-Area- Wjec-Eduqas Higher
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  18. Circles-Arcs-And-Sectors- Wjec-Eduqas Higher
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  19. Area-And-Perimeter- Wjec-Eduqas Higher
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  20. Circle-Theorems Wjec-Eduqas Higher
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  21. Bearings-Scale-Drawing-Constructions-And-Loci Wjec-Eduqas Higher
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  22. Angles-In-Polygons-And-Parallel-Lines Wjec-Eduqas Higher
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  23. Symmetry-And-Shapes Wjec-Eduqas Higher
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  24. Exchange-Rates-And-Best-Buys Wjec-Eduqas Higher
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  25. Standard-And-Compound-Units- Wjec-Eduqas Higher
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  26. Direct-And-Inverse-Proportion- Wjec-Eduqas Higher
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  27. Problem-Solving-With-Ratios Wjec-Eduqas Higher
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  28. Ratios Wjec-Eduqas Higher
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  29. Sequences Wjec-Eduqas Higher
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  30. Transformations-Of-Graphs- Wjec-Eduqas Higher
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  31. Graphing-Inequalities- Wjec-Eduqas Higher
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  32. Solving-Inequalities- Wjec-Eduqas Higher
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  33. Real-Life-Graphs Wjec-Eduqas Higher
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  34. Estimating-Gradients-And-Areas-Under-Graphs Wjec-Eduqas Higher
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  36. Graphs-Of-Functions Wjec-Eduqas Higher
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  37. Linear-Graphs Wjec-Eduqas Higher
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  38. Quadratic-Equations Wjec-Eduqas Higher
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  39. Linear-Equations- Wjec-Eduqas Higher
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  40. Algebraic-Proof Wjec-Eduqas Higher
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  41. Rearranging-Formulae Wjec-Eduqas Higher
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  42. Coordinate-Geometry- Wjec-Eduqas Higher
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  43. Functions Wjec-Eduqas Higher
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  44. Forming-And-Solving-Equations Wjec-Eduqas Higher
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  45. Iteration Wjec-Eduqas Higher
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  46. Simultaneous-Equations Wjec-Eduqas Higher
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  47. Algebraic-Fractions- Wjec-Eduqas Higher
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  48. Completing-The-Square Wjec-Eduqas Higher
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  49. Factorising Wjec-Eduqas Higher
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  50. Expanding-Brackets Wjec-Eduqas Higher
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  51. Algebraic-Roots-And-Indices Wjec-Eduqas Higher
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  52. Introduction-To-Algebra Wjec-Eduqas Higher
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  53. Using-A-Calculator Wjec-Eduqas Higher
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  54. Surds Wjec-Eduqas Higher
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  55. Rounding-Estimation-And-Bounds Wjec-Eduqas Higher
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  56. Fractions-Decimals-And-Percentages Wjec-Eduqas Higher
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  57. Simple-And-Compound-Interest-Growth-And-Decay Wjec-Eduqas Higher
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  58. Percentages Wjec-Eduqas Higher
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  59. Fractions Wjec-Eduqas Higher
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  60. Powers-Roots-And-Standard-Form Wjec-Eduqas Higher
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  61. Prime-Factors-Hcf-And-Lcm- Wjec-Eduqas Higher
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  62. Number-Operations Wjec-Eduqas Higher
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Exam code:C300

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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