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Basic Probability (Cambridge (CIE) IGCSE Maths)

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    What does the notation straight P open parentheses A close parentheses mean, in the context of probability?

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  • What does the notation straight P open parentheses A close parentheses mean, in the context of probability?

    straight P open parentheses A close parentheses is the notation for the probability of event A occurring.

  • True or False?

    Probabilities can only be expressed as fractions.

    False.

    Probabilities can be expressed as fractions, decimals or percentages.

  • What does it mean when two events are mutually exclusive.

    Mutually exclusive events are events that cannot both happen at the same time.

    E.g. when a dice is rolled, you cannot obtain a 6 and a 3 at the same time, therefore they are mutually exclusive events.

  • What is the complement of event A?

    The complement of event A is the event where event A does not happen.

    It is denoted by A to the power of apostrophe.

  • State an equation connecting straight P open parentheses A close parentheses and straight P open parentheses A to the power of apostrophe close parentheses.

    The key equation connecting straight P open parentheses A close parentheses and straight P open parentheses A to the power of apostrophe close parentheses is straight P open parentheses A close parentheses plus straight P open parentheses A to the power of apostrophe close parentheses equals 1.

    It can be rearranged as straight P open parentheses A to the power of apostrophe close parentheses equals 1 minus straight P open parentheses A close parentheses or straight P open parentheses A close parentheses equals 1 minus straight P open parentheses A to the power of apostrophe close parentheses.

  • True or False?

    There are only two possibilities in a lottery, 'win' and 'lose'.

    Therefore, the probability of winning is 1 half.

    False.

    The outcomes 'win' and 'lose' are not equally likely, so the probability of winning is not 1 half.

  • What is a sample space in the context of probability?

    A sample space is the set of all possible outcomes of an experiment.

    It may be a list or a grid showing all the possible outcomes.

  • True or False?

    You can always use a sample space grid to represent all possible outcomes.

    False.

    When combining more than two things, you may need to go back to listing outcomes instead of using a grid.

  • How do you calculate probabilities using a sample space?

    Count the possibilities you want, then divide by the total number of possibilities in the sample space.

    (Note: this only works if every possibility in the sample space is equally likely.)

  • Define relative frequency in the context of probability.

    In probability, relative frequency (also called experimental probability) is used to estimate probabilities from experimental data.

  • What is the equation used to calculate relative frequency?

    Relative frequency can be calculated using the following equation:

    Relative space frequency equals fraction numerator Number space of space successful space outcomes over denominator Total space number space of space trials end fraction

  • True or False?

    In order to estimate relative frequency in an experiment, each trial must have an equal chance of 'success'.

    True.

    In order to estimate relative frequency in an experiment, each trial must have an equal chance of 'success'. I.e. the trials are independent.

    E.g. when flipping a coin, getting a 'head' on one flip will not affect the chances of getting a 'head' on another flip.

    The trials are independent of each other and have an equal chance of success, therefore they can be used to estimate the relative frequency of getting a 'head'.

  • True or False?

    Calculating a relative frequency lets you know the exact probability.

    False.

    Relative frequency only provides an estimate for the true (or theoretical) probability.

  • Define expected frequency in the context of probability.

    Expected frequency refers to the number of times a particular outcome is expected to occur when repeating a trial numerous times.

  • How do you calculate the expected frequency of an event with probability p, if the experiment is repeated n times.

    To calculate the expected frequency of an event with probability p, if the experiment is repeated n times is, you must multiply the number of trials by the probability that the event will occur.

    Expected space frequency equals n p.

  • True or False?

    If an experiment is repeated many times, the number of occurrences of an event will always be exactly equal to the expected frequency.

    False.

    The number of occurrences tends to average out to the expected frequency over many repetitions, but may not be exactly equal.

  • True or false?

    Relative frequency and expected frequency can both take on any positive value.

    False.

    Expected frequency can in theory take on any positive value.

    But relative frequency is an estimate of a probability, so must be between 0 and 1.

  • True or false?

    A larger number of trials should give a more accurate result for relative frequency than a smaller number of trials.

    True.

    Usually a relative frequency calculated from a large number of trials is more reliable than one calculated from a small number of trials.

Previous:TransformationsNext:Probability Diagrams (Tree & Venn Diagrams)

    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