Start learning →

JEE Main Statistics and Probability — practice questions — page 3

Explore 179 free Statistics and Probability questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Statistics and Probability with Quill →

Statistics and Probability questions and exercises with answers

Showing questions 61–90 of 179.

In a factory, 60% of items come from Machine A and 40% from Machine B. 2% of A-items and 5% of B-items are defective. P(item from B | defective) is closest toRead the answer and worked solution →A random variable X counts the number of heads in 3 tosses of a fair coin. The mean E(X) isRead the answer and worked solution →The variance of the number of heads in 3 fair-coin tosses isRead the answer and worked solution →For a Binomial distribution B(n, p), the probability of exactly r successes isRead the answer and worked solution →A card is drawn at random from a well-shuffled deck of 52. E = "card is a face card" (King, Queen, Jack). P(E) equalsRead the answer and worked solution →E and F are independent events with P(E) = 0.3 and P(F) = 0.5. Then P(E ∪ F) equalsRead the answer and worked solution →Two dice are rolled. Let E = "sum is 8" and F = "at least one die shows 4". Then P(E|F) equalsRead the answer and worked solution →If P(A) = 0.4, P(B|A) = 0.5, then P(A ∩ B) equalsRead the answer and worked solution →For a random variable X, the variance Var(X) equalsRead 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 →Order the steps: compute a standard deviationRead the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Grouped data or ungrouped data?Read the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every statement true of the rangeRead the answer and worked solution →

Worked practice questions

In a factory, 60% of items come from Machine A and 40% from Machine B. 2% of A-items and 5% of B-items are defective. P(item from B | defective) is closest to

  1. 0.60
  2. 0.36
  3. 0.63
  4. 0.40
Show answer and solution

Correct answer: C. 0.63

1. P(A) = 0.6, P(B) = 0.4. P(D|A) = 0.02, P(D|B) = 0.05. 2. Total P(D) = 0.6 × 0.02 + 0.4 × 0.05 = 0.012 + 0.020 = 0.032. 3. P(B|D) = P(B) P(D|B) / P(D) = 0.020 / 0.032. 4. = 0.625, i.e. about 0.63. _Source: syllabus Mathematics, Ch 13 "Probability", §13.5_

Open this question →

A random variable X counts the number of heads in 3 tosses of a fair coin. The mean E(X) is

  1. 1
  2. 3
  3. 2
  4. 1.5
Show answer and solution

Correct answer: D. 1.5

1. X follows a Binomial distribution with n = 3, p = 1/2. 2. Mean of a Binomial random variable is E(X) = n × p. 3. So E(X) = 3 × 1/2 = 1.5. 4. Variance is n × p × q = 3 × 1/2 × 1/2 = 3/4. _Source: syllabus Mathematics, Ch 13 "Probability", §13.6_

Open this question →

The variance of the number of heads in 3 fair-coin tosses is

  1. 3/4
  2. 1/4
  3. 1
  4. 3/2
Show answer and solution

Correct answer: A. 3/4

1. n = 3, p = 1/2, q = 1 − p = 1/2. 2. For Binomial, variance = n × p × q. 3. = 3 × 1/2 × 1/2 = 3/4. 4. Standard deviation is √(3/4) = √3 / 2. _Source: syllabus Mathematics, Ch 13 "Probability", §13.6_

Open this question →

How to practise

  1. Choose a Statistics and Probability question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Statistics and Probability practice for JEE Main. Read explanations as you go. No signup form needed to start.

Practise Statistics and Probability →

More Mathematics topics

DeterminantsVector Algebra and 3D GeometryContinuity, Differentiability & DerivativesDifferential EquationsIntegrals and ApplicationsMatrices and DeterminantsRelations, Functions & Inverse TrigonometryStraight Lines and Conic Sections