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Conditional Probability (Cambridge (CIE) IGCSE Maths)

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  • What does the phrase "given that" typically indicate in a probability question?

    The phrase "given that" typically indicates a conditional probability question.

  • What is the notation for the conditional probability of event A occurring, given that event B has occurred?

    The notation for the conditional probability of event A occurring, given that event B has occurred, is straight P open parentheses A vertical line B close parentheses.

  • What might straight P open parentheses passes vertical line no space revision close parentheses mean in the context of a student preparing for an exam?

    straight P open parentheses passes vertical line no space revision close parentheses would be the probability that the student passes the exam, given that the student has done no revision.

  • State what "without replacement" means in the context of probability questions.

    "Without replacement" refers to situations where an item is drawn from a group and not returned before another draw is made.

  • True or False?

    Conditional probability questions always use the phrase "given that".

    False.

    Conditional probability questions do not always use the phrase "given that".

    The question may need to be interpreted to identify the conditional aspect.

  • What is the difference between straight P open parentheses A vertical line B close parentheses and straight P open parentheses B vertical line A close parentheses?

    The difference between straight P open parentheses A vertical line B close parentheses and straight P open parentheses B vertical line A close parentheses is this:

    • straight P open parentheses A vertical line B close parentheses is the probability that A happens, given that B has happened.

    • straight P open parentheses B vertical line A close parentheses is the probability that B happens, given that A has happened.

  • True or False?

    Conditional probability is only used in situations where things are drawn or selected without replacement.

    False.

    Conditional probability is used in situations where things are drawn or selected without replacement.

    However, it is also used in other situations where the outcome of one event affects the probabilities for another event occurring.

  • True or False?

    Combined conditional probability questions can involve using both the AND and OR rules from combined probability.

    True.

    Combined conditional probability questions can involve using both the AND and OR rules from combined probability.

  • True or False?

    In combined conditional probability questions, probabilities for subsequent events may change based on previous events.

    True.

    In combined conditional probability questions, probabilities for subsequent events may change based on previous events.

    E.g. if there are a number of yellow sweets and green sweets in a jar and two sweets are eaten, the probability of picking a yellow sweet will be different for the first and second picks.
    This is because there will be fewer sweets, and different numbers of each kind of sweet, after the first is picked.

  • True or False?

    Combined conditional probability questions can involve events happening simultaneously, or one after the other in a specific order.

    True.

    Combined conditional probability questions can involve events happening simultaneously, or one after the other in a specific order.

    However this does not change the mathematics of the question.

  • Why is it a good idea not to simplify any probability fractions until the very end of a question?

    Probabilities will often need to be added together to get to the final answer.

    This is easiest to do when they all have the same denominator.

Previous:Probability Diagrams (Tree & Venn Diagrams)Next:Averages & Range

    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 Toolkit

    6. Topic 6

      Percentages Toolkit

    7. Topic 7

      Simple & Compound Interest, Growth & Decay

    8. Topic 8

      Surds

    9. Topic 9

      Working with FDP

    10. Topic 10

      Working with Ratios

    11. Topic 11

      Compound Measures (Speed, Density, Pressure)

    12. Topic 12

      Time, Currency & Conversions

    13. Topic 13

      Rounding, Estimation & Bounds

    14. Topic 14

      Using a Calculator

    1. Topic 1

      Algebra Toolkit

    2. Topic 2

      Algebraic Roots & Indices

    3. Topic 3

      Expanding & Factorising Brackets

    4. Topic 4

      Linear Equations & Inequalities

    5. Topic 5

      Quadratic Equations

    6. Topic 6

      Rearranging Formulas

    7. Topic 7

      Simultaneous Equations

    8. Topic 8

      Algebraic Fractions

    9. Topic 9

      Forming & Solving Equations

    10. Topic 10

      Functions

    11. Topic 11

      Sequences

    12. Topic 12

      Proportion

    1. Topic 1

      Coordinate Geometry

    2. Topic 2

      Linear Graphs

    3. Topic 3

      Quadratic Graphs

    4. Topic 4

      Further Graphs & Tangents

    5. Topic 5

      Solving & Graphing Inequalities

    6. Topic 6

      Real-Life Graphs

    7. Topic 7

      Differentiation

    1. Topic 1

      Geometry Toolkit

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Constructions & Scale Drawings

    4. Topic 4

      Circle Theorems

    1. Topic 1

      Area & Perimeter

    2. Topic 2

      Circles, Arcs & Sectors

    3. Topic 3

      Volume & Surface Area

    4. Topic 4

      Congruence & Similarity

    1. Topic 1

      Right-Angled Triangles (Pythagoras & Trigonometry)

    2. Topic 2

      Sine, Cosine Rule & Area of Triangles

    3. Topic 3

      3D Pythagoras & Trigonometry

    4. Topic 4

      Trigonometric Graphs & Equations

    1. Topic 1

      Vectors

    2. Topic 2

      Transformations

    1. Topic 1

      Basic Probability

    2. Topic 2

      Probability Diagrams (Tree & Venn Diagrams)

    3. Topic 3

      Conditional Probability

    1. Topic 1

      Averages & Range

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency

    5. Topic 5

      Scatter Graphs & Correlation