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Mathematics - Probability

Practise 44 BITSAT previous year questions on Probability, compiled from papers spanning 2009 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty BITSAT tests.

Probability has been asked in 16 of the 16 years of BITSAT papers analysed (2009–2024), with 44 questions in all. 43% of them were easy, 48% moderate and 9% tough. Most of its questions came from 2023, with 7 questions that year. In the last three years (2022–2024) it had 14 questions across 6 papers, about 2.3 per paper.

The chapter's 9 topics are not weighted equally: Classical Definition of Probability (9 questions, 20%), Total Probability (9 questions, 20%), and Bernoulli Trial and Binomial Distribution (7 questions, 16%) have been asked the most. Classical Definition of Probability has also led over the last five years, with 4 questions. Bernoulli Trial and Binomial Distribution has produced the most tough questions (1).

  1. 1A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal2024 (Memory Based Paper 1)Total Probability
  2. 2For two events A and B , if and , then which of the following is not true?2024 (Memory Based Paper 1)Conditional Probability and Multiplication Theorem
  3. 3The probability that certain electronic component fails when first used is 0.10 . If it does not fail immediately, the probability that it l2024 (Memory Based Paper 2)Total Probability
  4. 4Given below is the distribution of a random variable If and , then2024 (Memory Based Paper 2)Bernoulli Trial and Binomial Distribution
  5. 5The probability of getting 10 in a single throw of three fair dice is2024 (Memory Based Paper 3)Classical Definition of Probability
  6. 6In a binomial distribution, the mean is 4 and variance is 3 . Then, its mode is2024 (Memory Based Paper 3)Bernoulli Trial and Binomial Distribution
  7. 7The probability of getting sum more than 7 when a pair of dice are thrown is:2023 (Memory Based Paper 1)Classical Definition of Probability
  8. 8The probability that a card drawn from a pack of 52 cards will be a diamond or king is:2023 (Memory Based Paper 1)Classical Definition of Probability
  9. 9Bag contains 6 red and 4 blue balls and bag contains 5 red and 6 blue balls. A ball is transferred from bag to bag and then a ball is drawn 2023 (Memory Based Paper 1)Total Probability
  10. 10If and , then2023 (Memory Based Paper 1)Conditional Probability and Multiplication Theorem
  11. 11If and are mutually exclusive events and if , then is equal to2023 (Memory Based Paper 2)Addition and Subtraction Theorems
  12. 12A coin is tossed twice. Then, the probability that atleast one tail occurs is2023 (Memory Based Paper 2)Classical Definition of Probability
  13. 13If and are events such that , then2023 (Memory Based Paper 2)Addition and Subtraction Theorems
  14. 14A six faced die is a biased one. It is thrice more likely to show an odd numbers than show an even number. It is thrown twice. The probabili2022Conditional Probability and Multiplication Theorem
  15. 15Girl students constitute of I year and of II year at Roorkee University. During summer holidays of the I year and of II year students are gi2021Baye's Theorem
  16. 16The mean and variance of a random variable having binomial distribution are 4 and 2 respectively, then is2021Random Variable and its Probability Distribution
  17. 17The probability that certain electronic component fails when first used is 0.10 . If it does not fail immediately, the probability that it l2020Total Probability
  18. 18A die is thrown 7 times. What is the probability that an even number turns up at least 4 times?2019Classical Definition of Probability
  19. 19Three numbers are chosen at random without replacement from { 1 , 2 , 3 , , 8 } . The probability that their minimum is 3 , given that their2019Classical Definition of Probability
  20. 20Cards are drawn one by one at random from a well shuffled pack of 52 cards until 2 aces are obtained for the first time. The probability tha2019Classical Definition of Probability
  21. 21The sum of mean and variance of a Binomial distribution B D for 3 trials is 2 . 7 , then the binomial distribution B D is given by2018Random Variable and its Probability Distribution
  22. 22Let A and B are two independent events. If the probability that both A and B occur together is 1 6 and the probability that neither of them 2018Independent Events
  23. 23In a test an examiner either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he/she2018Baye's Theorem
  24. 24If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 22017Conditional Probability and Multiplication Theorem
  25. 25A coin is tossed 7 times. Each time a man calls head. The probability that he wins the toss at least four times is2017Bernoulli Trial and Binomial Distribution
  26. 26A man takes a step forward with probability 0.4 and backward with probability 0.6 . The probability that at the end of eleven steps he is on2016Bernoulli Trial and Binomial Distribution
  27. 27A bag contains coins. It is known that n of these coins have a head on both sides, whereas the remaining coins are fair. A coin is picked up2015Total Probability
  28. 28A bag contains 3 red and 3 white balls. Two balls are drawn one by one. The probability that they are of different colours is.2015Total Probability
  29. 29If in a binomial distribution , then equals2015Bernoulli Trial and Binomial Distribution
  30. 30A bag contains 5 brown and 4 white socks. man pulls out 2 socks. Find the probability that they are of the same colour.2014Total Probability
  31. 31A bag contains coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected 2014Total Probability
  32. 32A coin is tossed 7 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.2014Bernoulli Trial and Binomial Distribution
  33. 33For the box contains red balls and white balls. Let and box is selected at random and a ball is drawn from it. If a red ball is drawn, then 2013Conditional Probability and Multiplication Theorem
  34. 34The probability of India winning a test match against West Indies is . Assuming independence from match to match, the probability that in a 2013Total Probability
  35. 35The probability of simultaneous occurrence of atleast one of two events and is If the probability that exactly one of occurs is then is equa2012Addition and Subtraction Theorems
  36. 36A boy is throwing stones at a target. The probability of hitting the target at any trial is The probability of hitting the target 5 th time 2012Classical Definition of Probability
  37. 37Two dice are thrown together 4 times. The probability that both dice will show same numbers twice is -2012Bernoulli Trial and Binomial Distribution
  38. 38If \(A\) and \( {B}\) are mutually exclusive events and if \( {P}( {B})= {1}{3}, {P}( {A} {B})= {13}{21}\), then \( {P}( {A})\) is equal to2011Addition and Subtraction Theorems
  39. 39A die is loaded such that the probability of throwing the number \(i\) is proportional to its reciprocal. The probability that 3 appears in 2011Addition and Subtraction Theorems
  40. 40If the mean, mode and S.D. of a frequency distribution are 41, 45 and 8 respectively, then its Pearson's coefficient of skewness is2010Classical Definition of Probability
  41. 41The equation of the plane containing the line \( { {x}- {x}_1}{ }= { {y}- {y}_1}{ {~m}}= { {z}- {z}_1}{ {n}}\) is \(a (x-x_1 )+b (y-y_1 )+c 2010Geometric Probability
  42. 42If mean of a poisson distribution of a random variable \(X\) is 2 , then the value of \(P(X > 1.5)\) is2010Independent Events
  43. 43A line segment has length 63 and direction ratios are \(3,-2,6\). If the line makes an obtuse angle with \( {x}\)-axis, the components of th2009Conditional Probability and Multiplication Theorem
  44. 44It is given that the events \(A\) and \(B\) are such that \(P(A)= {1}{4}, P(A B)= {1}{2} \) and \( P(B A)= {2}{3}\). Then \(P(B)\) is2009Geometric Probability

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 44 questions compiled from BITSAT papers spanning 2009 to 2024.

2.Are these questions only from BITSAT, or from other exams too?

These are BITSAT questions specifically for the Probability chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Probability an important chapter for BITSAT Mathematics?

Probability has appeared in 16 of the 16 years of BITSAT papers covered here, with 44 questions across 19 papers - about 2 per paper it appears in.

4.What is the difficulty level of Probability questions in BITSAT?

Of the 44 questions analysed for this chapter, 43% are easy, 48% moderate and 9% tough. 2023 had the most, with 7 questions.

5.Which topics in Probability should I focus on?

These topics have carried the most weightage in Probability:

  • Classical Definition of Probability - 9 questions (20%)
  • Total Probability - 9 questions (20%)
  • Bernoulli Trial and Binomial Distribution - 7 questions (16%)
  • Bernoulli Trial and Binomial Distribution has produced the most tough questions (1).
6.Is Probability's weightage in BITSAT going up or down?

Across all 19 papers analysed, Probability has averaged about 2.3 questions per paper. In the last three years (2022–2024), that average has stayed about the same, at about 2.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.