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GCSEMathsAQAHigherFlashcards5. ProbabilityCombined & Conditional Probability

Combined & Conditional Probability (AQA GCSE Maths)

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  • FrontCombined Probabilities

    What does AND mean for combined probabilities?

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  • What does AND mean for combined probabilities?

    AND means multiply (cross times) and is used for independent events to find the probability of both events occurring.

    E.g. the probability of events A and B occurring is straight P open parentheses A close parentheses cross times straight P open parentheses B close parentheses.

  • What does OR mean for combined probabilities?

    OR means add (+) and is used for mutually exclusive events to find the probability of one event or the other event occurring.

    E.g. the probability of either event A and/or event B occurring is straight P open parentheses A close parentheses plus straight P open parentheses B close parentheses.

  • True or False?

    The sum of all probabilities is 1.

    True.

    As long as the possibilities considered are all mutually exclusive (non-overlapping), then the sum of all probabilities is 1.

  • State the equation for the probability of two independent events, A and B, occurring together.

    If A and B are independent events, then the probability of both events occurring is:

    straight P open parentheses A space and space B close parentheses equals straight P open parentheses A close parentheses cross times straight P open parentheses B close parentheses.

  • State the equation for the probability of one or the other of two mutually exclusive events, A and B, occurring.

    If A and B are mutually exclusive events, then the probability of one or the other of them occurring is:

    straight P open parentheses A space or space B close parentheses equals straight P open parentheses A close parentheses plus straight P open parentheses B close parentheses.

  • 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:Tree DiagramsNext:Averages, Ranges & Data

    1. Topic 1

      Number Operations

    2. Topic 2

      Prime Factors, HCF & LCM

    3. Topic 3

      Powers, Roots & Standard Form

    4. Topic 4

      Fractions

    5. Topic 5

      Percentages

    6. Topic 6

      Simple & Compound Interest, Growth & Decay

    7. Topic 7

      Fractions, Decimals & Percentages

    8. Topic 8

      Rounding, Estimation & Bounds

    9. Topic 9

      Surds

    10. Topic 10

      Using a Calculator

    1. Topic 1

      Introduction to Algebra

    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

      Linear Equations

    10. Topic 10

      Quadratic Equations

    11. Topic 11

      Simultaneous Equations

    12. Topic 12

      Iteration

    13. Topic 13

      Forming & Solving Equations

    14. Topic 14

      Functions

    15. Topic 15

      Coordinate Geometry

    16. Topic 16

      Linear Graphs

    17. Topic 17

      Graphs of Functions

    18. Topic 18

      Equation of a Circle

    19. Topic 19

      Estimating Gradients & Areas under Graphs

    20. Topic 20

      Real-Life Graphs

    21. Topic 21

      Solving Inequalities

    22. Topic 22

      Graphing Inequalities

    23. Topic 23

      Transformations of Graphs

    24. Topic 24

      Sequences

    1. Topic 1

      Ratios

    2. Topic 2

      Problem Solving with Ratios

    3. Topic 3

      Direct & Inverse Proportion

    4. Topic 4

      Standard & Compound Units

    5. Topic 5

      Exchange Rates & Best Buys

    1. Topic 1

      Symmetry & Shapes

    2. Topic 2

      Angles in Polygons & Parallel Lines

    3. Topic 3

      Bearings, Scale Drawing, Constructions & Loci

    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

      Pythagoras & Trigonometry

    11. Topic 11

      Sine, Cosine Rule & Area of Triangles

    12. Topic 12

      3D Pythagoras & Trigonometry

    13. Topic 13

      Vectors

    14. Topic 14

      Transformations

    1. Topic 1

      Introduction to Probability

    2. Topic 2

      Simple Probability Diagrams

    3. Topic 3

      Tree Diagrams

    4. Topic 4

      Combined & Conditional Probability

    1. Topic 1

      Averages, Ranges & Data

    2. Topic 2

      Statistical Diagrams

    3. Topic 3

      Histograms

    4. Topic 4

      Cumulative Frequency & Box Plots

    5. Topic 5

      Scatter Graphs & Correlation