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ECZ Grade 12 School Certificate Probability Density Function — practice questions

Explore 28 free Probability Density Function questions in ECZ Grade 12 School Certificate Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Probability Density Function questions and exercises with answers

Showing questions 1–28 of 28.

Match each probability word to its meaningRead the answer and worked solution →Judge each probability claimRead the answer and worked solution →Complete the definition of conditional probabilityRead the answer and worked solution →True or false: conditional probabilityRead the answer and worked solution →Independent or mutually exclusive?Read the answer and worked solution →Match each rule to its nameRead the answer and worked solution →IndependenceRead the answer and worked solution →Order the steps for a Bayes' theorem questionRead the answer and worked solution →Complete the conditions for a partitionRead the answer and worked solution →True or false: independence versus exclusivityRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Tap every statement that follows from independenceRead the answer and worked solution →The multiplication ruleRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Complete the theorem of total probabilityRead the answer and worked solution →Which theorem answers which question?Read the answer and worked solution →True or false: total probability and BayesRead the answer and worked solution →Match each historical figure to their contributionRead the answer and worked solution →The Historical NoteRead the answer and worked solution →Flip and pair: notation with meaningRead the answer and worked solution →Order the reasoning: from a partition to a posteriorRead the answer and worked solution →Tap every quantity that is a probabilityRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →Assertion and reason: the multiplication ruleRead the answer and worked solution →True or false: the Historical NoteRead the answer and worked solution →Sort each statement by which idea it describesRead the answer and worked solution →

Worked practice questions

Match each probability word to its meaning

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Matching pairs
  1. Left
    Sample space
    Right
    All possible outcomes of an experiment
  2. Left
    Event
    Right
    A set of outcomes of an experiment
  3. Left
    Union
    Right
    Outcomes in at least one of the events
  4. Left
    Intersection
    Right
    Outcomes that occur in all the events
  5. Left
    Outcome
    Right
    One observation of a random process
  6. Left
    Complement
    Right
    The outcomes left outside an event
Instructions
Tap a word on the left, then tap the meaning on the right that goes with it.
_Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 10: Probability_

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Judge each probability claim

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Questions
  1. Statement is true
    Yes
    Statement
    Mutually exclusive events can never happen at the same time.
  2. Statement is true
    No
    Statement
    One experiment can have several different sample spaces.
  3. Statement is true
    Yes
    Statement
    Independent events tell you nothing about one another.
  4. Statement is true
    Yes
    Statement
    Relative frequency divides the times an event occurred by the number of trials.
  5. Statement is true
    No
    Statement
    A tree diagram is the quickest way to handle independent events.
  6. Statement is true
    Yes
    Statement
    A two way contingency table also records the totals for each event.
  7. Statement is true
    No
    Statement
    Complementary events can both occur on the same trial.
Instructions
Tap True or False for each statement about events and their probabilities.
_Source: Siyavula Mathematics Grade 11 (CC BY 4.0), Chapter 10 Probability_

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Complete the definition of conditional probability

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Missing parts
  1. Answer
    P(F)
    Choices
    1. P(F)
    2. P(E)
    3. P(E ∪ F)
  2. Answer
    not zero
    Choices
    1. not zero
    2. equal to 1
    3. less than P(E)
  3. Answer
    0 and 1
    Choices
    1. 0 and 1
    2. −1 and 1
    3. 0 and P(F)
Complete the statement
P(E|F) is defined as P(E ∩ F) divided by {0}, and it is only defined when P(F) is {1}. Its value always lies between {2}.
The definition the whole chapter is built on, including the condition that makes it meaningful. Source: syllabus Maths Part II, Ch 13 Probability.

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ProbabilityBinomial TheoremCorrelation and RegressionGeometryMeanMedianPermcombPermutations and Combinations