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Indian Navy SSR Probability — practice questions

Explore 31 free Probability questions in Indian Navy SSR 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 1–30 of 31.

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 →Conditional probability P(A | B) is defined as:Read the answer and worked solution →In a survey, 60% read newspaper A, 40% read B, 20% read both. P(reading neither):Read the answer and worked solution →Two cards drawn from a deck (no replacement). P(both kings):Read the answer and worked solution →The probability of getting a number greater than 6 in a single roll of a die 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 →

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. $1.25$
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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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Conditional probability P(A | B) is defined as:

  1. P(A and B) / P(B) (with P(B) > 0)
  2. P(A) - P(B)
  3. P(A) × P(B)
  4. P(A or B)
Show answer and solution

Correct answer: A. P(A and B) / P(B) (with P(B) > 0)

P(A|B) = P(A and B) / P(B). Probability of A given B has occurred. For independent events, P(A|B) = P(A).

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In a survey, 60% read newspaper A, 40% read B, 20% read both. P(reading neither):

  1. 10%
  2. 20%
  3. 30%
  4. 40%
Show answer and solution

Correct answer: B. 20%

P(A or B) = P(A) + P(B) - P(A and B) = 60 + 40 - 20 = 80%. P(neither) = 1 - 80% = 20%.

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