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Agniveer Air Force Sequences and Series — practice questions — page 2

Explore 75 free Sequences and Series questions in Agniveer Air Force Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sequences and Series questions and exercises with answers

Showing questions 31–60 of 75.

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 →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 →

Worked practice questions

True or false: conditional probability

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Questions
  1. Statement is true
    Yes
    Statement
    P(E|F) = P(E ∩ F) ÷ P(F), provided P(F) ≠ 0.
  2. Statement is true
    No
    Statement
    P(E|F) can be greater than 1.
  3. Statement is true
    Yes
    Statement
    P(E′|F) = 1 − P(E|F).
  4. Statement is true
    No
    Statement
    P(E|F) is defined even when P(F) = 0.
  5. Statement is true
    Yes
    Statement
    0 ≤ P(E|F) ≤ 1 always holds.
Each line is a summary bullet, quoted or bent. Source: syllabus Maths Part II, Ch 13 Probability.

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Independent or mutually exclusive?

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Items
  1. Item
    P(E ∩ F) = P(E) P(F)
    Category
    Independent
  2. Item
    P(E|F) = P(E)
    Category
    Independent
  3. Item
    Knowing F changes nothing about E
    Category
    Independent
  4. Item
    E and F cannot both occur
    Category
    Mutually exclusive
  5. Item
    P(E ∩ F) = 0
    Category
    Mutually exclusive
  6. Item
    The events have no outcome in common
    Category
    Mutually exclusive
Categories
  1. Item
    Independent
  2. Item
    Mutually exclusive
These are different ideas that get confused constantly. Independent events satisfy P(E ∩ F) = P(E)P(F) mutually exclusive events cannot both happen, so their intersection is empty. Source: syllabus Maths Part II, Ch 13 Probability.

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Match each rule to its name

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Matching pairs
  1. Left
    P(E|F) = P(E ∩ F) ÷ P(F)
    Right
    conditional probability
  2. Left
    P(E ∩ F) = P(E) P(F|E)
    Right
    multiplication rule
  3. Left
    P(A) = ΣP(Eᵢ) P(A|Eᵢ)
    Right
    theorem of total probability
  4. Left
    P(Eᵢ|A) from P(A|Eᵢ)
    Right
    Bayes' theorem
The four named results of the chapter. Source: syllabus Maths Part II, Ch 13 Probability.

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