5.3.10

Conditional Probability Venn Diagrams

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Conditional Probability

The conditional probability of an event A is the probability of event A happening given that event B has already happened. Event A given event B can be written as A|B.

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Conditional probability

  • The general equation for conditional probability is above.
  • If events A and B are independent then P(A|B) = P(A).
  • For events that are dependent:
    • P(A and B) = P(A) × P(B|A)
    • or P(A and B) = P(B) × P(A|B)
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Venn diagrams

  • To calculate the conditional probability P(A|B) from a Venn diagram, divide the number of elements in the set AB by the number of elements in B.
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Two-way tables

  • Count the number of cells that show both event A and event B occurring.
  • Divide this by the number of cells that show event B occurring.
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Tree diagrams

  • The probabilities in a tree diagram are often dependent.
    • I.e. the probability of the second event depends on the result of the first event.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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