Welcome to **AMBiPi (**Read as**: एम्बीपाई) (Amans Maths Blogs)**. JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get * JEE Main Math Previous Year Paper Probability Questions Answer Keys Solutions*.

### JEE Mains Mathematics Probability Questions Bank

**JEE Probability Questions No:1**

A dice is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of is

**[2002]**

**Option A**: 8 / 3

**Option B**: 3 / 8

**Option C**: 4 / 5

**Option D**: 5 / 4

**Show/Hide Answer Key**

**Option D: 5 / 4**

**JEE Main Probability Questions No:2**

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is (1 / 2), (1 / 3), and (1 / 4). Probability that the problem is solved is

**[2002]**

**Option A**: 3 / 4

**Option B**: 1 / 2

**Option C**: 2 / 3

**Option D**: 1 / 3

**Show/Hide Answer Key**

**Option A: 3 / 4**

**JEE Mathematics Probability Questions No:3**

A and B are events such that P (AUB) = (3/4). P (A ∩ B) = (1/4), P(**A**)= (2/3) then P(**A ∩ **B) is

**[2002]**

**Option A**: 5/12

**Option B**: 3/8

**Option C**: 5/8

**Option D**: 1/4

**Show/Hide Answer Key**

**Option A: 5/12**

**JEE Main Math Probability Questions No:4**

The mean and variance of a random variable X having binomial distribution are 4 and 2 respectively, then P (X = 1) is

**[2003]**

**Option A**: 1 / 4

**Option B**: 1 / 32

**Option C**: 1 / 16

**Option D**: 1 / 8

**Show/Hide Answer Key**

**Option B: 1 / 32**

**Probability JEE Questions No:5**

Events A, B, C are mutually exclusive events such that P (A) = (3X + 1 / 3), P (B) = (1 – x / 4 ) and P (C) = (1 – 2x / 2).The set of possible values of x are in the interval

**[2003]**

**Option A**: [ (1/3), (1/2) ]

**Option B**: [ (1/3), (2/3) ]

**Option C**: [ (1/3), (13/3) ]

**Option D**: [ 0, 1 ]

**Show/Hide Answer Key**

**Option C: [ (1/3), (13/3) ]**

**Probability JEE Main Questions No:6**

Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is

**[2003]**

**Option A**: 4/5

**Option B**: 3/5

**Option C**: 1/5

**Option D**: 2/5

**Show/Hide Answer Key**

**Option D: 2/5**

**Probability Questions for JEE Mains Questions No: 7**

A random variable X has the probability distribution:

For the events E = { X is a prime number } and F = {X < 4}, the P(E ∪ F) is

**[2004]**

**Option A**: 0.50

**Option B**: 0.77

**Option C**: 0.35

**Option D**: 0.87

**Show/Hide Answer Key**

**Option B: 0.77**

**Probability Questions and Answers No:8**

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

**[2004]**

**Option A**: 28 / 256

**Option B**: 219 / 256

**Option C**: 128 / 256

**Option D**: 37 / 256

**Show/Hide Answer Key**

**Option A: 28 / 256**

**Probability Questions with Solutions No:9**

The probability that A speaks truth is (4/5) while the probability for B is (3/4). The probability that they contradict each other when asked to speak on a fact is

**[2004]**

**Option A**: 4/5

**Option B**: 1/5

**Option C**: 7/20

**Option D**: 3/20

**Show/Hide Answer Key**

**Option C: 7/20**

**JEE Mains Probability Questions No: 10**

A random variable X has Poisson distribution with mean 2 Then P (X > 1.5) equals

**[2005]**

**Option A**: 2 / e^{2}

**Option B**: 0

**Option C**: 1 – (3 / e^{2)}

**Option D**: 3 / e^{2}

**Show/Hide Answer Key**

**Option C: 1 – (3 / e ^{2})**

**JEE Mains Math Probability Questions No: 11**

Let A and B be two events such that P (**A ∪ B**) = (1/6) , P (A ∩ B) = (1/4) and P(**A**) = (1/4), where **A **stands for complement of event A. Then events A and B are

**[2005]**

**Option A**: Equally likely and mutually exclusive

**Option B**: Equally likely but not independent

**Option C**: Independent but not equally likely

**Option D**: Mutually exclusive and independent

**Show/Hide Answer Key**

**Option C: Independent but not equally likely**

**Probability Questions for JEE Questions No: 12**

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

**[2005]**

**Option A**: 2/9

**Option B**: 1/9

**Option C**: 8/9

**Option D**: 7/9

**Show/Hide Answer Key**

**Option B: 1/9**

**Probability Problems for Class 11 Questions No:13**

At a telephone enquiry system the number of phone calls regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10 minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is

**[2006]**

**Option A**: 6 / 5^{e}

**Option B**: 5 / 6

**Option C**: 6 / 55

**Option D**: 6 / e^{5}

**Show/Hide Answer Key**

**Option D: A6 / e ^{5}**

**Probability Problems for Class 12 Questions No: 14**

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

**[2007]**

**Option A**: 8 / 729

**Option B**: 8 / 243

**Option C**: 1 / 729

**Option D**: 8 / 9

**Show/Hide Answer Key**

**Option B: 8 / 243**

**Probability Problems for Class 11 JEE Questions No: 15**

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

**[2007]**

**Option A**: 0.2

**Option B**: 0.7

**Option C**: 0.06

**Option D**: 0.14

**Show/Hide Answer Key**

**Option D: 0.14**

**Probability Problems for Class 12 JEE Questions No:16**

It 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) is

**[2008]**

**Option A**: 1/6

**Option B**: 1/3

**Option C**: 2/3

**Option D**: 1/2

**Show/Hide Answer Key**

**Option B: 1/3**

**JEE Probability Questions No:17**

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A U B) is

**[2008]**

**Option A**: 3/5

**Option B**: 0

**Option C**: 1

**Option D**: 2/5

**Show/Hide Answer Key**

**Option C: 1**

**JEE Main Probability Questions No:18**

In a binomial distribution B (n, p = (1/4) ), if the probability of at least one success is greater than equal (9/ 10) to then n is greater than:

**[2009]**

**Option A**: 1 / log_{10} 4 + log_{10} 3

**Option B**: 9 / log_{10} 4 – log_{10} 3

**Option C**: 4 / log_{10} 4 – log_{10} 3

**Option D**: 1 / log_{10} 4 – log_{10} 3

**Show/Hide Answer Key**

**Option D: 1 / log _{10} 4 – log_{10} 3 **

**JEE Mathematics Probability Questions No:19**

One ticket is selected at random from 50 tickets numbered 00,01,02,…,49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals:

**[2009]**

**Option A**: 1/7

**Option B**: 5/14

**Option C**: 1/50

**Option D**: 1/14

**Show/Hide Answer Key**

**Option D: 1/14**

**JEE Main Math Probability Questions No:20**

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

**[2010]**

**Option A**: 36

**Option B**: 66

**Option C**: 108

**Option D**: 3

**Show/Hide Answer Key**

**Option C: 108**

**Probability JEE Questions No:21**

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the um. The probability that the three balls have different colour is

**[2010]**

**Option A**: 2/7

**Option B**: 1/21

**Option C**: 2/23

**Option D**: 1/3

**Show/Hide Answer Key**

**Option A: 2/7**

**Probability JEE Main Questions No:22**

Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to (31/32) then p lies in the interval

**[2011]**

**Option A**: (3/4, 11/12]

**Option B**: [0, 1/2]

**Option C**: (11/12, 1]

**Option D**: (1/2, 3/4]

**Show/Hide Answer Key**

**Option B: [0, 1/2]**

**Probability Questions for JEE Mains Questions No: 23**

Let A, B, C be pairwise independent events with P(C) > 0 and P(A ∩ B ∩ C) = 0. Then P(A^{C} ∩ B^{C} | C) is equal to

**[2011]**

**Option A**: P(A^{C} ) – P(B^{C})

**Option B**: P(A^{C} ) – P(B)

**Option C**: P(A) – P(B^{C})

**Option D**: P(A^{C} ) + P(B^{C})

**Show/Hide Answer Key**

**Option B: P (A ^{C}) – P(B)**

**Probability Questions and Answers No: 24**

Three numbers are chosen at random without replacement from (1,2,3,..8). The probability that their minimum is 3, given that their maximum is 6 is

**[2012]**

**Option A**: 3/8

**Option B**: 1/5

**Option C**: 1/4

**Option D**: 2/5

**Show/Hide Answer Key**

**Option B: 1/5**

**Probability Questions with Solutions No: 25**

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is:

**[2013]**

**Option A**: 17 / 3^{5}

**Option B**: 13 / 3^{5}

**Option C**: 11 / 3^{5}

**Option D**: 10 / 3^{5}

**Show/Hide Answer Key**

**Option C: 11 / 3 ^{5}**

**JEE Mains Probability Questions No: 26**

Given two independent events, if the probability that exactly one of them occurs is (26/49) and the probability that none of them occurs is (15/49) then the probability of more probable of the two events is:

**[2013]**

**Option A**: 4/7

**Option B**: 6/7

**Option C**: 3/7

**Option D**: 5/7

**Show/Hide Answer Key**

**Option A: 4/7**

**JEE Mains Math Probability Questions No: 27**

If X has a binomial distribution, B(n, p) with parameters n and p such that P (X = 2) = P (X = 3), then E (X), the mean of variable X, is

**[2014]**

**Option A**: 2 – p

**Option B**: 3 – p

**Option C**: p / 2

**Option D**: p / 3

**Show/Hide Answer Key**

**Option B: 3 – p**

**Probability Questions for JEE Questions No: 28**

Let A and E be any two events with positive probabilities

Statement-1: P(E / A) ≥ P(A / E) P(E)

Statement-2: P(A / E) ≥ P(A E)

**[2014]**

**Option A**: Both the statements are true

**Option B**: Both the statements are false

**Option C**: Statement-1 is true, Statement-2 is false

**Option D**: Statement-1 is false, Statement-2 is true

**Show/Hide Answer Key**

**Option A: Both the statements are true**

**Probability Problems for Class 11 Questions No:29**

Let A and B be two events such that P(**A U B**) = (1/6), P(**A ∩ B**) = (1/4), and P(A) = (1/4) where **A** stands for the complement of the event A. Then the events A and B are

**[2014]**

**Option A**: Independent but not equally likely.

**Option B**: Independent and equally likely.

**Option C**: Mutually exclusive and independent.

**Option D**: Equally likely but not independent

**Show/Hide Answer Key**

**Option A: Independent but not equally likely **

**Probability Problems for Class 12 Questions No: 30**

If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one is :

**[2015]**

**Option A**: 9 / 16

**Option B**: 3 / 4

**Option C**: 1 / 16

**Option D**: 15 / 16

**Show/Hide Answer Key**

**Option D: 15 / 16**

JEE Main Mathematics Previous Year Questions with Solutions: Algebra |

JEE Main Previous Year Mathematics Questions Set, Relations & Functions | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Complex Numbers | 1 to 30 | 31 to 60 | 61 to 81 | |

JEE Main Previous Year Mathematics Questions Sequence & Series| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Quadratic Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Permutations & Combinations| 1 to 30 | 31 to 60 | 61 to 94 | |

JEE Main Previous Year Mathematics Questions Binomial Theorems| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Determinants & Matrices| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Trigonometry |

JEE Main Previous Year Mathematics Questions Trigonometry Ratios Identities| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Properties of Triangles| 1 to 31 | |

JEE Main Previous Year Mathematics Questions Trigonometrical Equations| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Inverse Trigonometrical Functions| 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Height & Distance| 1 to 27 | |

JEE Main Mathematics Previous Year Questions with Solutions: Coordinate Geometry |

JEE Main Previous Year Mathematics Questions Cartesian System & Straight Lines | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Circles | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Parabola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Ellipse | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Hyperbola | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Limit, Continuity & Differentiability | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Differentiations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Application of Derivative | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Integral Calculus |

JEE Main Previous Year Mathematics Questions Indefinite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Definite Integrals | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Area By Integration | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Differential Equations |

JEE Main Previous Year Mathematics Questions Differential Equations | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Vector & 3D Geometry |

JEE Main Previous Year Mathematics Questions Vectors | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 139 | |

JEE Main Previous Year Mathematics Questions 3D Geometry | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Mathematics Previous Year Questions with Solutions: Statistics & Probability |

JEE Main Previous Year Mathematics Questions Statistics | 1 to 30 | 31 to 60 | 61 to 86 | |

JEE Main Previous Year Mathematics Questions Probability | 1 to 30 | 31 to 60 | 61 to 95 | |

JEE Main Mathematics Previous Year Questions with Solutions: Miscellaneous |

JEE Main Previous Year Mathematics Questions Mathematical Induction | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |

JEE Main Previous Year Mathematics Questions Mathematical Reasoning | 1 to 30 | 31 to 60 | 61 to 90 | 91 to 120 | 121 to 150 | |