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Assam CEE Probability — practice questions — page 3

Explore 80 free Probability questions in Assam CEE 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 61–80 of 80.

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

Complete the conditions for a partition

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Missing parts
  1. Answer
    pairwise disjoint
    Choices
    1. pairwise disjoint
    2. independent
    3. equally likely
  2. Answer
    sample space
    Choices
    1. sample space
    2. event A
    3. unit interval
  3. Answer
    nonzero
    Choices
    1. nonzero
    2. equal
    3. small
Complete the statement
For Bayes' theorem the events E₁ … Eₙ must be {0}, their union must be the whole {1}, and each must have {2} probability.
Bayes' theorem needs a genuine partition, and the conditions are exactly these. Source: syllabus Maths Part II, Ch 13 Probability.

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True or false: independence versus exclusivity

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Questions
  1. Statement is true
    No
    Statement
    Independent and mutually exclusive mean the same thing.
  2. Statement is true
    Yes
    Statement
    For independent events, P(E ∩ F) = P(E) P(F).
  3. Statement is true
    Yes
    Statement
    For mutually exclusive events, P(E ∩ F) = 0.
  4. Statement is true
    Yes
    Statement
    Knowing F occurred leaves P(E) unchanged when E and F are independent.
  5. Statement is true
    No
    Statement
    Mutually exclusive events with nonzero probabilities are independent.
The trap round. Two events that cannot occur together are as far from independent as it gets. Source: syllabus Maths Part II, Ch 13 Probability.

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Assertion and reason

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Questions
  1. Reason
    P(F) sits in the denominator of the definition.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    P(E|F) requires P(F) ≠ 0.
  2. Reason
    The denominator sums over every branch, so the branches must cover S once.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    Bayes' theorem needs the events to form a partition.
  3. Reason
    Mutually exclusive events satisfy P(E ∩ F) = 0.
    Verdict
    The assertion is false and the reason is true.
    Assertion
    Two mutually exclusive events with nonzero probability are independent.
  4. Reason
    Conditioning on F still leaves a complete probability model.
    Verdict
    Both are true; the reason explains the assertion.
    Assertion
    P(E′|F) = 1 − P(E|F).
The reason must actually explain the assertion. Source: syllabus Maths Part II, Ch 13 Probability.

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