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UPCET / UPSEE Probability & Statistics — practice questions — page 4

Explore 138 free Probability & Statistics questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Probability & Statistics questions and exercises with answers

Showing questions 91–120 of 138.

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 →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead 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 →Order the steps: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →

Worked practice questions

Two are true, one is not

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Questions
  1. False statement
    P(E|F) may exceed 1
    Statements
    1. P(E|F) needs P(F) ≠ 0
    2. P(E′|F) = 1 − P(E|F)
    3. P(E|F) may exceed 1
  2. False statement
    Bayes' theorem requires all branches to be equally likely
    Statements
    1. Bayes' theorem requires all branches to be equally likely
    2. Bayes' theorem needs a partition of the sample space
    3. Total probability sums P(Eᵢ)P(A|Eᵢ) over the partition
  3. False statement
    Mutually exclusive always implies independent
    Statements
    1. Independent events satisfy P(E ∩ F) = P(E)P(F)
    2. Mutually exclusive always implies independent
    3. Mutually exclusive events satisfy P(E ∩ F) = 0
The false line is always a condition dropped or swapped. Source: syllabus Maths Part II, Ch 13 Probability.

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Three of these are wrong. Find the one that holds.

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Questions
  1. Question
    Three of these statements about P(E|F) are false.
    Choices
    1. Item
      It equals P(E ∩ F) ÷ P(F)
      Correct
      Yes
    2. Explanation
      That is P(F|E), the other way round.
      Item
      It equals P(F ∩ E) ÷ P(E)
    3. Explanation
      It needs P(F) ≠ 0.
      Item
      It is defined for any F
    4. Explanation
      Every probability lies in [0, 1].
      Item
      It can exceed 1
  2. Question
    Three of these statements about independence are false.
    Choices
    1. Item
      P(E ∩ F) = P(E) P(F)
      Correct
      Yes
    2. Explanation
      That is mutual exclusivity, not independence.
      Item
      P(E ∩ F) = 0
    3. Explanation
      The product rule is for intersection.
      Item
      P(E ∪ F) = P(E) P(F)
    4. Explanation
      That describes mutually exclusive events.
      Item
      Independent events cannot both occur
Each wrong option is a genuine exam trap: an inverted conditional, a dropped condition, or exclusivity mistaken for independence. Source: syllabus Maths Part II, Ch 13 Probability.

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Complete the theorem of total probability

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Missing parts
  1. Answer
    partition
    Choices
    1. partition
    2. sequence
    3. sample
  2. Answer
    P(A|Eᵢ)
    Choices
    1. P(A|Eᵢ)
    2. P(Eᵢ|A)
    3. P(A) P(Eᵢ)
Complete the statement
If E₁ … Eₙ form a {0} of the sample space and each has nonzero probability, then for any event A, P(A) is the sum of P(Eᵢ) times {1}.
The statement as printed in the summary. Source: syllabus Maths Part II, Ch 13 Probability.

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