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OJEE Statistics and Probability — practice questions — page 2

Explore 70 free Statistics and Probability questions in OJEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Statistics and Probability questions and exercises with answers

Showing questions 31–60 of 70.

For Poisson distribution with rate λ: P(X = k) =Read the answer and worked solution →Three-card hand probability of a flush (any same suit):Read the answer and worked solution →At least one '6' in 4 throws of a fair die:Read the answer and worked solution →Variance of fair die roll (1-6):Read the answer and worked solution →P(A) = 1/3, P(B) = 1/2, P(A ∩ B) = 1/6. P(A ∪ B) =Read the answer and worked solution →From 7 men and 5 women, choose committee of 4 with at least 1 woman:Read the answer and worked solution →A box has 6 balls, 4 are red. Two balls drawn (without replacement). P(both red):Read the answer and worked solution →Mean Square Error (MSE) of estimator decomposes as:Read the answer and worked solution →Properties of normal distribution: ___ % of data within 1 SD of mean.Read the answer and worked solution →X ~ Binomial(50, 0.4). Find E[X] and Var[X]:Read the answer and worked solution →For two events A and B, P(A | B) = 0.6, P(B) = 0.5, P(A) = 0.4. P(B | A) =Read the answer and worked solution →Mean Absolute Deviation (MAD):Read the answer and worked solution →Chebyshev's inequality: P(|X - μ| ≥ kσ) ≤Read the answer and worked solution →Two independent X, Y with Var(X) = 4, Var(Y) = 9. Var(X + Y) =Read the answer and worked solution →Tap every measure of dispersion your syllabus listsRead the answer and worked solution →Central tendency or dispersion?Read the answer and worked solution →Complete the definition of rangeRead the answer and worked solution →Working out a rangeRead the answer and worked solution →Order the argument: why mean deviation uses absolute valuesRead the answer and worked solution →True or false: why plain deviations failRead the answer and worked solution →Complete the definition of mean deviationRead the answer and worked solution →Match each measure to how it is builtRead the answer and worked solution →True or false: variance and standard deviationRead the answer and worked solution →Squared or absolute?Read the answer and worked solution →Reading the definitions backRead the answer and worked solution →True or false: what this chapter coversRead 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: compute a mean deviation about the meanRead the answer and worked solution →

Worked practice questions

For Poisson distribution with rate λ: P(X = k) =

  1. e^(-λ) λ^k / k!
  2. λ × k
  3. λ^k
  4. C(n,k) λ^k
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Correct answer: A. e^(-λ) λ^k / k!

Poisson(λ): P(X = k) = e^(-λ) λ^k / k! for k = 0, 1, 2, ... Models rare events in fixed time (radioactive decays, traffic accidents). Mean = λ. Variance = λ.

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Three-card hand probability of a flush (any same suit):

  1. 1/4
  2. 4 × C(13,3)/C(52,3) = 4 × 286/22100 = 0.0518
  3. 1/13
  4. 1/52
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Correct answer: B. 4 × C(13,3)/C(52,3) = 4 × 286/22100 = 0.0518

**Suits:** 4 choices. **Flush:** 3 cards same suit: C(13,3) = 286. Total: C(52,3) = 22100. P = 4 × 286/22100 = 1144/22100 ≈ 0.0518.

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At least one '6' in 4 throws of a fair die:

  1. 4/6
  2. 2/6
  3. 1 - (5/6)⁴ ≈ 0.518
  4. 2/3
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Correct answer: C. 1 - (5/6)⁴ ≈ 0.518

Complementary: P(no 6 in 4) = (5/6)⁴ = 625/1296. P(at least one 6) = 1 - 625/1296 = 671/1296 ≈ 0.518.

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More Mathematics topics

SequencesProbability & StatisticsBinomial TheoremSequences and SeriesGeometryLinear ProgrammingLimits and ContinuityPermutations and Combinations