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VITEEE Probability & Statistics — practice questions — page 3

Explore 117 free Probability & Statistics questions in VITEEE 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 61–90 of 117.

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 →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 →

Worked practice questions

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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Independence

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Questions
  1. Question
    If E and F are independent, P(E ∩ F) equals
    Choices
    1. P(E) + P(F)
    2. P(E) P(F)
    3. 0
    Correct choice
    P(E) P(F)
  2. Question
    If E and F are independent, P(E|F) equals
    Choices
    1. P(F)
    2. 1
    3. P(E)
    Correct choice
    P(E)
  3. Question
    If E and F are independent, P(F|E) equals
    Choices
    1. P(F)
    2. P(E)
    3. 0
    Correct choice
    P(F)
  4. Question
    Mutually exclusive events have P(E ∩ F) equal to
    Choices
    1. P(E)P(F)
    2. 0
    3. 1
    Correct choice
    0
Independence can be written three equivalent ways, and your syllabus lists all three. Source: syllabus Maths Part II, Ch 13 Probability.

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Order the steps for a Bayes' theorem question

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Steps
  1. Identify the events that partition the sample space
  2. Write down the prior probability of each partition event
  3. Write the probability of the observed event given each of them
  4. Combine them by the theorem of total probability to get P(A)
  5. Divide the one branch you want by that total to get P(Eᵢ|A)
The route the chapter uses: identify the partition, write the priors, write the conditionals, total them then divide. Source: syllabus Maths Part II, Ch 13 Probability.

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