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UCE (O-Level) Probability — practice questions

Explore 33 free Probability questions in UCE (O-Level) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Probability questions and exercises with answers

Showing questions 1–30 of 33.

The set of all possible results of an experiment is given which name?Read the answer and worked solution →A die is rolled and lands showing five. What is that single result called?Read the answer and worked solution →When every outcome is equally likely, the theoretical probability of an event is which ratio?Read the answer and worked solution →How is the relative frequency of an event worked out?Read the answer and worked solution →The union of two sets contains which elements?Read the answer and worked solution →A single cupcake is taken from a packet. Event A is that it is vanilla and event B is that it is red velvet. What are these two events?Read the answer and worked solution →An event and its complement together cover the whole sample space and never overlap. What do their two probabilities do?Read 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 →

Worked practice questions

The set of all possible results of an experiment is given which name?

  1. The sample space
  2. The event set
  3. The outcome set
  4. The trial list
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Correct answer: A. The sample space

1. An experiment refers to an uncertain process, such as tossing a coin. 2. The sample space of an experiment is the set of all possible outcomes of that experiment. 3. For a single coin toss the sample space holds just heads and tails. 4. An event is only the particular set of outcomes you happen to be interested in. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 14: Probability_

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A die is rolled and lands showing five. What is that single result called?

  1. An event set
  2. An outcome
  3. A sample space
  4. A trial run
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Correct answer: B. An outcome

1. Rolling the die is the uncertain process, which is the experiment. 2. An outcome of an experiment is a single result of that experiment. 3. Landing on five is one such single result, so it is an outcome. 4. The sample space would be all six faces the die could have shown. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 14: Probability_

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When every outcome is equally likely, the theoretical probability of an event is which ratio?

  1. Sample size over event size
  2. Event size over trial count
  3. Event size over sample size
  4. Trial count over event size
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Correct answer: C. Event size over sample size

1. Theoretical probability can only be used when all outcomes are equally likely. 2. It is the ratio between the number of outcomes in the event set and the number in the sample space. 3. The event set is always part of the sample space, so this ratio never exceeds one. 4. Turning the ratio upside down would give values above one, which no probability can take. _Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 14: Probability_

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