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Probability Diagrams - Venn & Tree Diagrams (Edexcel IGCSE Maths A)

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  • FrontProbabilities from Venn Diagrams

    Describe how to find straight P open parentheses A close parentheses from a Venn diagram that shows sets A and B.

    E.g. find straight P open parentheses A close parentheses from the Venn diagram.

    Venn diagram with sets A and B. Set A only has 8, the intersection of sets A and B has 2 and set B only has 15. Within the universal set, U, but outside both sets A and B is 7.

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  • Describe how to find straight P open parentheses A close parentheses from a Venn diagram that shows sets A and B.

    E.g. find straight P open parentheses A close parentheses from the Venn diagram.

    Venn diagram with sets A and B. Set A only has 8, the intersection of sets A and B has 2 and set B only has 15. Within the universal set, U, but outside both sets A and B is 7.

    straight P open parentheses A close parentheses is the probability of being in set A.

    This is the number inside the full circle of set A divided by the total number of the whole Venn diagram, e.g. straight P open parentheses A close parentheses equals fraction numerator 8 plus 2 over denominator 8 plus 2 plus 15 plus 7 end fraction equals 10 over 32.

    Venn diagram with two intersecting circles labelled A and B. Set A only contains 8 the intersection contains 2 and set B only contains 15. The number 7 lies within the universal set, U, but outside both sets A and B. The whole of set A is highlighted green.

  • Describe how to find straight P open parentheses A intersection B close parentheses from a Venn diagram that shows sets A and B.

    E.g. find straight P open parentheses A intersection B close parentheses from the Venn diagram.

    Venn diagram with sets A and B. Set A only has 8, the intersection of sets A and B has 2 and set B only has 15. Within the universal set, U, but outside both sets A and B is 7.

    straight P open parentheses A intersection B close parentheses is the probability of being in the intersection of set A and set B.

    This is the value inside the overlapping region of set A and set B divided by the total number of the whole Venn diagram, e.g. straight P open parentheses A intersection B close parentheses equals fraction numerator 2 over denominator 8 plus 2 plus 15 plus 7 end fraction equals 2 over 32.

    Venn diagram with two intersecting circles labelled A and B. Set A only contains 8 the intersection contains 2 and set B only contains 15. The number 7 lies within the universal set, U, but outside both sets A and B. The intersection of set A and B is highlighted.

  • True or False?

    If A and B are mutually exclusive, then straight P open parentheses A intersection B close parentheses equals 0.

    True.

    If A and B are mutually exclusive, then straight P open parentheses A intersection B close parentheses equals 0.

    On a Venn diagram, if A and B are mutually exclusive then their circles do not overlap (they cannot both happen at the same time).

    This makes being in the intersection impossible, so straight P open parentheses A intersection B close parentheses equals 0.

  • True or False?

    To find straight P open parentheses A union B close parentheses you need to double-count the numbers in the intersection (overlap) as they occur twice.

    False.

    To find straight P open parentheses A union B close parentheses you do not double-count the numbers in the intersection A intersection B, you just count them once.

  • Describe which region on a Venn diagram is required to calculate straight P open parentheses A intersection B intersection C close parentheses.

    E.g. find straight P open parentheses A intersection B intersection C close parentheses from the Venn diagram.

    Venn diagram with three overlapping circles labelLed A, B, and C. Regions contain numbers 5, 2, 11, 6, 3, 1, 9, and 8. U is the universal set.

    The region required to calculate straight P open parentheses A intersection B intersection C close parentheses is the one that is the overlap of all three sets A, B and C. E.g. straight P open parentheses A intersection B intersection C close parentheses equals fraction numerator 3 over denominator 5 plus 2 plus 11 plus 6 plus 3 plus 1 plus 9 plus 8 end fraction equals 3 over 45.

    Venn diagram with three circles labelled A, B, and C. Numbers inside segments: A-5, B-11, C-9, AB-2, AC-6, BC-1, ABC-3. Inside the universal set but outside sets A, B and C is the number 8. The intersection between all three circles is highlighted.

  • True or False?

    On a Venn diagram showing sets A and B, the region required to calculate straight P open parentheses A apostrophe close parentheses is the part of set B that does not overlap A.

    False.

    On a Venn diagram showing sets A and B, the region required to calculate straight P open parentheses A apostrophe close parentheses is anything that is outside the circle of A, e.g.

    Venn diagram with two intersecting circles labelled A and B. Set A only contains 8 the intersection contains 2 and set B only contains 15. The number 7 lies within the universal set, U, but outside both sets A and B. The whole of the universal set, except for set A, is highlighted green.

  • On a Venn diagram showing sets A and B, explain how to calculate straight P open parentheses A vertical line B close parentheses.

    E.g. find straight P open parentheses A vertical line B close parentheses from the Venn diagram.

    Venn diagram with sets A and B. Set A only has 8, the intersection of sets A and B has 2 and set B only has 15. Within the universal set, U, but outside both sets A and B is 7.

    straight P open parentheses A vertical line B close parentheses is a conditional probability meaning the probability of being in A, given that you are in B. Therefore the probability is out of set B only.

    The only part of set A in set B is A intersection B, so divide the number in A intersection B by the total number in B, e.g. straight P open parentheses A vertical line B close parentheses equals fraction numerator 2 over denominator 2 plus 15 end fraction equals 2 over 17.

    Venn diagram with two intersecting circles labelled A and B. Set A only contains 8 the intersection contains 2 and set B only contains 15. The number 7 lies within the universal set, U, but outside both sets A and B. Set B is highlighted as is the section of set A that lies within set B.

  • True or False?

    To find the probability of A and B using a probability tree diagram, you add the probabilities on the branches for A and B.

    False.

    To find the probability of A and B using a probability tree diagram, you do not add the probabilities on the branches for A and B.

    To find the probability of A and B, you multiply along the branches.

  • True or False?

    The probabilities on all of the branches in a probability tree diagram should add up to 1.

    False.

    The probabilities on all of the branches in a probability tree diagram should not add up to 1.

    The probabilities on any set of branches (usually a pair) should add up to 1.

  • True or False?

    The sum of the probabilities of all of the final outcomes on a probability tree diagram should be equal to 1.

    True.

    The sum of the probabilities of all of the final outcomes on a probability tree diagram should be equal to 1.

  • A tree diagram is used to represent two events, A and B, where each event has three possible outcomes, 1, 2 and 3.

    How many possible final outcomes are there?

    For a tree diagram used to represent two events, where each events has three possible outcomes, there are nine possible final outcomes (32 = 9).

    Tree diagram displaying events A and B. Each event has three outcomes, 1, 2 and 3. These lead to 9 final outcomes: 11, 12, 13, 21, 22, 23, 31, 32 and 33.

  • A tree diagram is used to represent three tennis matches, where each event has two possible outcomes: player A winning or player B winning.

    How many possible final outcomes are there?

    A tree diagram is used to represent three tennis matches, where each event has two possible outcomes: player A winning or player B winning.

    There are eight possible final outcomes (23 = 8).

    The eight outcomes are AAA, AAB, ABA, ABB, BAA, BAB, BBA, BBB.

    Tree diagram displaying events 1, 2 and 3. Each event has two outcomes, A and B. These lead to 8 final outcomes: AAA, AAB, ABA, ABB, BAA, BAB, BBA and BBB.
Previous:Probability ToolkitNext:Combined & Conditional Probability

    1. Topic 1

      Number Toolkit

    2. Topic 2

      Set Notation & Venn Diagrams

    3. Topic 3

      Prime Factors, HCF & LCM

    4. Topic 4

      Powers, Roots & Standard Form

    5. Topic 5

      Fractions

    6. Topic 6

      Percentages

    7. Topic 7

      Compound Interest & Depreciation

    8. Topic 8

      Fractions, Decimals & Percentages

    9. Topic 9

      Rounding, Estimation & Bounds

    10. Topic 10

      Surds

    11. Topic 11

      Using a Calculator

    12. Topic 12

      Ratio Toolkit

    13. Topic 13

      Ratio Problem Solving

    14. Topic 14

      Exchange Rates & Best Buys

    15. Topic 15

      Direct & Inverse Proportion

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding Brackets

    4. Topic 4

      Factorising

    5. Topic 5

      Completing the Square

    6. Topic 6

      Algebraic Fractions

    7. Topic 7

      Rearranging Formulas

    8. Topic 8

      Algebraic Proof

    9. Topic 9

      Solving Linear Equations

    10. Topic 10

      Solving Quadratic Equations

    11. Topic 11

      Solving Inequalities

    12. Topic 12

      Simultaneous Equations

    13. Topic 13

      Forming & Solving Equations

    1. Topic 1

      Sequences

    2. Topic 2

      Functions

    3. Topic 3

      Coordinate Geometry

    4. Topic 4

      Linear Graphs y = mx + c

    5. Topic 5

      Graphs of Functions

    6. Topic 6

      Estimating Gradients

    7. Topic 7

      Real-Life Graphs

    8. Topic 8

      Graphing Inequalities

    9. Topic 9

      Transformations of Graphs

    10. Topic 10

      Differentiation

    1. Topic 1

      Standard & Compound Units

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing & Constructions

    4. Topic 4

      Circle Theorems

    5. Topic 5

      Area & Perimeter

    6. Topic 6

      Circles, Arcs & Sectors

    7. Topic 7

      Volume & Surface Area

    8. Topic 8

      Congruence, Similarity & Geometrical Proof

    9. Topic 9

      Area & Volume of Similar Shapes

    10. Topic 10

      Right-Angled Triangles - Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Statistics Toolkit

    2. Topic 2

      Histograms

    3. Topic 3

      Cumulative Frequency Diagrams

    4. Topic 4

      Probability Toolkit

    5. Topic 5

      Probability Diagrams - Venn & Tree Diagrams

    6. Topic 6

      Combined & Conditional Probability