NDA Probability questions with solutions
Probability and distributions. 27 questions from our 2016–2025 NDA pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.
Also practise: Probability for JEE Main · Probability for JEE Advanced · Probability for CAT
NDA 2025
- A fair die is thrown once. The probability of getting a prime number or a multiple of 3 is
- A letter is chosen at random from the letters of the word MATHEMATICS. The probability that it is a vowel is
- A fair die is rolled twice. The probability that the number on the second roll is strictly greater than the number on the first is
- The events A and B are independent when P(A∩ B)=P(A)P(B). 2. Whenever P(A)>0 and P(B)>0, the conditional probabilities P(Amid B) and P(Bmid A) are…
NDA 2024
- A bag contains 5 red and 3 green balls. Two balls are drawn at random without replacement. The probability that they are of different colours is
- If A and B are independent events with P(A)=1/3 and P(B)=1/4, then P(A∪ B) is equal to
- A number is selected at random from the integers 1 to 30. The probability that it is a multiple of 3 or of 5 is
- Let A and B be events of a sample space with P(A)>0 and P(B)>0. 1. If A and B are independent, then P(A∩ B)=P(A)P(B). 2. If A and B are independent…
NDA 2023
NDA 2022
NDA 2021
NDA 2020
- Two fair dice are thrown together. The probability that the product of the numbers on them is 12 is
- A box contains 4 white and 6 black balls. Three balls are drawn at random without replacement. The probability that exactly two are white is
- If P(A)=0.6, P(B)=0.3 and the events A and B are independent, then P(A∪ B) is
- Urn U1 contains 4 red and 2 black balls, and urn U2 contains 1 red and 5 black balls. An urn is chosen at random and a ball drawn from it is red. The…
- For events A and B: 1. If A and B are mutually exclusive and both have non-zero probability, they cannot be independent. 2. P(A∪ B)=P(A)+P(B) for any…
NDA 2019
- A card is drawn from a well-shuffled pack of 52 cards. The probability that it is a face card or a spade is
- Three letters are placed at random into three addressed envelopes, one in each. The probability that none of the letters goes into its own envelope is
- Events A and B are independent with P(A)=1/3 and P(B)=1/4. The probability that neither of them occurs is
- Machines A and B produce 60% and 40% of the items in a factory, and 2% and 5% of their output respectively is defective. An item picked at random is…
- For any event A, P(A)+P(bar A)=1. 2. If A⊂ B, then P(A)≥ P(B).
NDA 2017
- A number is chosen at random from the integers 1 to 30. The probability that it is divisible by 4 or by 6 is
- A and B are events with P(A)=0.6, P(Bmid A)=0.5 and P(Bmid A^c=0.2. Then P(B) equals
- In a family of three children, the probability that there is at least one boy and at least one girl is (assuming equal chances for each)
- Examine the following assertions about any two events A and B of a sample space: 1. P(A∪ B)≤ P(A)+P(B). 2. P(A∩ B)≥ P(A).
NDA 2016
Other Mathematics topics
Three Dimensional Geometry 48Vector Algebra 60Complex Numbers and Quadratic Equations 35Binomial Theorem 16Sequences and Series 36Quadratic Equations 27Permutations and Combinations 25Statistics 35Matrices 37Determinants 13Sets, Relations and Functions 39Binary Number System 11Logarithms 11Inverse Trigonometric Functions 22Trigonometric Functions and Identities 49Trigonometric Equations 16Properties of Triangles 18Heights and Distances 12Straight Lines 43Circles 21Conic Sections 28Limits 23Continuity and Differentiability 16Application of Derivatives 34Derivatives 33Integrals 16Definite Integrals 23Application of Integrals 12Differential Equations 30