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Indian Navy MR Probability — practice questions

Explore 28 free Probability questions in Indian Navy MR 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 1–28 of 28.

For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:Read the answer and worked solution →Median of an odd-length sorted data set is: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 →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

For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:

  1. $1$
  2. $0$
  3. $2.0$
  4. $1.25$
Show answer and solution

Correct answer: D. $1.25$

$F(0.5) = 3(0.5) - 2(0.5)^3 = 1.5 - 2(0.125) = 1.5 - 0.25 = 1.25$. (Note: this exceeds 1, which signals a problem with the source p.d.f. — but the question is purely about evaluating the given $F$ formula.)

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Median of an odd-length sorted data set is:

  1. First value
  2. Middle value (n+1)/2 th term
  3. Last value
  4. Average of first and last
Show answer and solution

Correct answer: B. Middle value (n+1)/2 th term

For odd n, median = middle value at position (n+1)/2. For even n, median = average of n/2 and (n/2 + 1) values.

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Complete the definition of conditional probability

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Missing parts
  1. Answer
    P(F)
    Choices
    1. P(F)
    2. P(E)
    3. P(E ∪ F)
  2. Answer
    not zero
    Choices
    1. not zero
    2. equal to 1
    3. less than P(E)
  3. Answer
    0 and 1
    Choices
    1. 0 and 1
    2. −1 and 1
    3. 0 and P(F)
Complete the statement
P(E|F) is defined as P(E ∩ F) divided by {0}, and it is only defined when P(F) is {1}. Its value always lies between {2}.
The definition the whole chapter is built on, including the condition that makes it meaningful. Source: syllabus Maths Part II, Ch 13 Probability.

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