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 Probability Questions Answer Keys Solutions*.

### JEE Mains Mathematics Probability Questions Bank

**Probability Problems for Class 11 Questions No: 61**

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is

**[2019]**

**Option A**: 1/11

**Option B**: 1/10

**Option C**: 1/12

**Option D**: 1/17

**Show/Hide Answer Key**

**Option A: 1/11**

**Probability Problems for Class 12 Questions No: 62**

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is (1/4). If the probability that at most two machines will be out of service on the same day is (3/4)^{3}k, then k is equal to:

**[2020]**

**Option A**: 17 / 8

**Option B**: 17 / 4

**Option C**: 17 / 2

**Option D**: 4

**Show/Hide Answer Key**

**Option A: 17 / 8**

**Probability Problems for Class 11 JEE Questions No: 63**

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value -1. Then the expected value of X, is:

**[2020]**

**Option A**: 3 / 16

**Option B**: 1 / 8

**Option C**: -3 / 16

**Option D**: -1 / 8

**Show/Hide Answer Key**

**Option B: 1 / 8**

**Probability Problems for Class 12 JEE Questions No: 64**

A random variable X has the following probability distribution:

Then, P(X > 2) is equal to:

**[2020]**

**Option A**: 7 / 12

**Option B**: 1 / 36

**Option C**: 1 / 6

**Option D**: 23 / 36

**Show/Hide Answer Key**

**Option D: 23 / 36**

**JEE Probability Questions No: 65**

The probability of a man hitting a target is (1/10). The least number of shots required, so that the probability of his hitting the target at least once is greater than (1/4) is

**[2020]**

**Show/Hide Answer Key**

**Correct Ans : 3**

**JEE Main Probability Questions No: 66**

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is

**[2020]**

**Show/Hide Answer Key**

**Correct Ans : 11**

**JEE Mathematics Probability Questions No: 67**

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is

**[2020]**

**Show/Hide Answer Key**

**Correct Ans : 11**

**JEE Main Math Probability Questions No:68**

Let A and B be two independent events such that P(A) = (1/3) and P(B) = (1/6) Then, which of the following is TRUE?

**[2020]**

**Option A**: P(A / B) = (2/3)

**Option B**: P(A / B’) = (1/3)

**Option C**: P(A’ / B’) = (1/3)

**Option D**: P(A / (A ∪ B )) = (1/4)

**Show/Hide Answer Key**

**Option B: P(A / B’) = (1/3)**

**Probability JEE Questions No: 69**

In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is

**[2020]**

**Option A**: 9/16

**Option B**: 11/16

**Option C**: 13/16

**Option D**: 15/16

**Show/Hide Answer Key**

**Option B: 11/16**

**Probability JEE Main Questions No: 70**

Let E^{C} denote the complement of an event E. Let E_{1}, E_{2}, and E_{3}, be any pairwise independent events with P(E_{1}) > 0 and P(E_{1} ∩ E_{2} ∩ E_{3}) = 0 Then P(E^{C}_{2 }∩ E^{C}_{3 }/ E_{1}) is equal to

**[2020]**

**Option A**: P(E^{C}_{2 }) + P(E_{3})

**Option B**: P(E^{C}_{3 }) – P(E^{C}_{2 })

**Option C**: P(E_{3})) – P(E^{C}_{2})

**Option D**: P(E^{C}_{3 }) – P(E_{2})

**Show/Hide Answer Key**

**Option D: P(E ^{C}_{3}) – P(E_{2})**

**Probability Questions for JEE Mains Questions No: 71**

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to 50. A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box l is

**[2020]**

**Option A**: 2/3

**Option B**: 8/17

**Option C**: 4/17

**Option D**: 2/5

**Show/Hide Answer Key**

**Option B: 8/17**

**Probability Questions and Answers No: 72**

The probability that a randomly chosen 5-digit number is made from exactly two digits is made from exactly two digits is

**[2020]**

**Option A**: 135/10^{4}

**Option B**: 121/10^{4}

**Option C**: 150/10^{4}

**Option D**: 134/10^{4}

**Show/Hide Answer Key**

**Option A: 135/10 ^{4}**

**Probability Questions with Solutions No: 73**

A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is

**[2020]**

**Option A**: 1/4

**Option B**: 1/3

**Option C**: 1/8

**Option D**: 1/9

**Show/Hide Answer Key**

**Option D: 1/9**

**JEE Mains Probability Questions No: 74**

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before 4 throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is

**[2020]**

**Option A**: 5/31

**Option B**: 31/61

**Option C**: 5/6

**Option D**: 30/61

**Show/Hide Answer Key**

**Option D: 30/61**

**JEE Mains Math Probability Questions No: 75**

Let in a binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then the probability of getting exactly 3 successes is equal to

**[2021]**

**Option A**: 80 / 243

**Option B**: 32 / 625

**Option C**: 40 / 243

**Option D**: 128 / 625

**Show/Hide Answer Key**

**Option B: 32 / 625**

**Probability Questions for JEE Questions No: 76**

A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability P(X ≥ 5 | X > 2) is:

**[2021]**

**Option A**: 125 / 216

**Option B**: 11 / 36

**Option C**: 5 / 6

**Option D**: 25 / 36

**Show/Hide Answer Key**

**Option D: 25 / 36**

**Probability Problems for Class 11 Questions No: 77**

The probability distribution of random variable X is given by:

Let p = P(1 < X < 4 | X < 3). If 5p = λK, then λ equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 30**

**Probability Problems for Class 12 Questions No: 78**

The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5) have exactly two elements in their intersection, is

**[2021]**

**Option A**: 65/2^{7}

**Option B**: 65/2^{8}

**Option C**: 135/2^{9}

**Option D**: 35/2^{7}

**Show/Hide Answer Key**

**Option C: 135/2 ^{9}**

**Probability Problems for Class 11 JEE Questions No: 79**

Let B_{i},(i = 1, 2, 3) be three independent events in a sample space. The probability that only β, occur is α. Only B_{2}, occurs is β and only B_{3}, occurs is ɣ. Let p be the probability that none of the events B_{i} occurs and these 4 probabilities satisfy the equations (α-2β) p = αβ and (β – 3ɣ) p = 2βɣ (All the probabilities are assumed to lie in the interval (0, 1)). Then ( P(B_{1}) / P(B_{3}) ) is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans: 6**

**Probability Problems for Class 12 JEE Questions No: 80**

Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen element of A leaves remainder 2 when divided by 5 is

**[2021]**

**Option A**: 2/9

**Option B**: 97/297

**Option C**: 122/297

**Option D**: 1/5

**Show/Hide Answer Key**

**Option B: 97/297**

**JEE Probability Questions No: 81**

When a missile is fired a ship, the probability that it is intercepted is (1/3) and the probability that the missile hits the target, given that it is not intercepted, is (3/4). If three missiles are fired independently from the ship, then the probability that all three hit the target, is

**[2021]**

**Option A**: 1/27

**Option B**: 3/8

**Option C**: 3/4

**Option D**: 1/8

**Show/Hide Answer Key**

**Option D: 1/8**

**JEE Main Probability Questions No: 82**

A seven digit number is formed using digits 3, 3, 4, 4, 4, 5, 5. The probability, that number so formed is divisible by 2, is

**[2021]**

**Option A**: 1/7

**Option B**: 6/7

**Option C**: 4/7

**Option D**: 3/7

**Show/Hide Answer Key**

**Option D: 3/7**

**JEE Mathematics Probability Questions No: 83**

A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is

**[2021]**

**Option A**: 15/2^{13}

**Option B**: 15/2^{12}

**Option C**: 15/2^{8}

**Option D**: 15/2^{14}

**Show/Hide Answer Key**

**Option A: 15/2 ^{13}**

**JEE Main Math Probability Questions No: 84**

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is

**[2021]**

**Option A**: 52/867

**Option B**: 22/425

**Option C**: 3/4

**Option D**: 39/50

**Show/Hide Answer Key**

**Option D: 39 / 50**

**Probability JEE Questions No: 85**

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be (1/2) and probability of occurrence of 0 at the odd place be (1/3). Then the probability that ’10’ is followed by ’01’ is equal to

**[2021]**

**Option A**: 1/18

**Option B**: 1/3

**Option C**: 1/6

**Option D**: 1/9

**Show/Hide Answer Key**

**Option D: 1/9**

**Probability JEE Main Questions No: 86**

Let there be three independent events E_{1}, E_{2} and E_{3}. The probability that only E_{1}, occurs is ⍺, only E_{2}, occurs is β and only E_{3}, occurs is ɣ. Let ‘p’ denote the probability of none of events occurs that satisfies the equations (⍺ – 2β)p = ⍺β and (β – 3ɣ)p = 2βɣ. All the given probabilities are assumed to lie in the interval (0, 1).Then, (Probability of occurrence of E_{1} / Probability of occurrence of E_{3}) is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 6**

**Probability Questions for JEE Mains Questions No: 87**

Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 – k), the probability that exactly one of B and C occurs is (1 – 2k), the probability that exactly one of C and A occurs is (1 – k) and the, probability of all A, B and C occur simultaneously is k^{2},where 0 < k < 1. Then the probability that at least one of A, B and C occur is

**[2021]**

**Option A**: Greater than (1/8) but less than (1/4)

**Option B**: Greater than (1/2)

**Option C**: Greater than (1/4) but less than (1/2)

**Option D**: Exactly equal to (1/2)

**Show/Hide Answer Key**

**Option B: Greater than (1/2)**

**Probability Questions and Answers No: 88**

Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is

**[2021]**

**Option A**: 1/66

**Option B**: 1/11

**Option C**: 1/9

**Option D**: 2/11

**Show/Hide Answer Key**

**Option B: 1/11**

**Probability Questions with Solutions No: 89**

Four dice are thrown simultaneously and the numbers shown on these dice are recorded in 2 × 2 matrices. The probability that such formed matrices have all different 7 entries and are non-singular, is

**[2021]**

**Option A**: 45/162

**Option B**: 23/81

**Option C**: 22/81

**Option D**: 43/162

**Show/Hide Answer Key**

**Option D: 43/162**

**JEE Mains Probability Questions No: 90**

A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 4**

**JEE Mains Math Probability Questions No: 91**

A student appeared in an examination consisting of 8 true false type questions. The students guesses the answers with equal probability. The smallest value of n, so that the probability of guessing at least ‘n’ correct answers is less than is

**[2021]**

**Option A**: 5

**Option B**: 6

**Option C**: 3

**Option D**: 4

**Show/Hide Answer Key**

**Option A: 5**

**Probability Questions for JEE Questions No: 92**

The probability that a randomly selected 2-digit number belongs to the set (n ∈ N : (2^{n} – 2) is a multiple of 3} is equal to

**[2021]**

**Option A**: 1/6

**Option B**: 2/3

**Option C**: 1/2

**Option D**: 1/3

**Show/Hide Answer Key**

**Option C: 1/2**

**Probability Problems for Class 11 Questions No: 93**

When a certain biased die is rolled, a particular face occurs with probability (1/6) – x and its opposite face occurs with probability (1/6) + x. All other faces occur with probability (1/6). Note that opposite faces sum to 7 in any die. If 0 < x < (1/6) , and the probability of obtaining total sum = 7, when such a die is rolled twice, is (13/96) , then the value of x is:

**[2021]**

**Option A**: 1/16

**Option B**: 1/8

**Option C**: 1/9

**Option D**: 1/12

**Show/Hide Answer Key**

**Option B: 1/8**

**Probability Problems for Class 12 Questions No: 94**

Let S = {1, 2, 3, 4, 5, 6). Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is

**[2021]**

**Option A**: 1/10

**Option B**: 1/15

**Option C**: 1/5

**Option D**: 1/30

**Show/Hide Answer Key**

**Option A: 1/10**

**Probability Problems for Class 11 JEE Questions No: 95**

An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98 p is equal to

**[2021]**

**Show/Hide Answer Key**

**Correct Ans : 28**

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 | |