Probability Questions with Solutions
Probability measures how likely an event is, as a number between 0 and 1. It equals the number of favourable outcomes divided by the total number of possible outcomes, when all outcomes are equally likely. This topic covers coins, dice, playing cards, drawing balls from a bag, complementary events, independent events, and conditional probability. The most useful tools are the complement rule (P(at least one) = 1 - P(none)) and the multiplication rule for independent events. For engineering and MCA entrance exams, the topic also includes the addition theorem, conditional probability, Bayes' theorem, and probability distributions. A clear sample space is the key to avoiding mistakes, so always list or count all outcomes carefully. Practise the probability questions below. Each comes with a step-by-step solution that shows how the sample space and favourable outcomes are counted.
- Q21.
A four-digit number is formed using the digits 1, 2, 3, 4, 5 without repetition. The probability that it is divisible by 3 is
A. B. C. D.mediumAsked in NIMCET 2022View solution āŗ - Q22.
There are two circles in the xy-plane whose equations are and . A point is chosen at random inside the larger circle. Then the probability that the point has been taken from the smaller circle is
A. B. C. D.mediumAsked in NIMCET 2022View solution āŗ - Q23.
If a fair die is rolled successively, then the probability that 1 appears for the first time in an even-numbered throw is
A. B. C. D.mediumAsked in NIMCET 2015View solution āŗ - Q24.
A is targeting B, B and C are targeting A. Probabilities of hitting the target by A, B and C are , and respectively. If A is hit, then the probability that B hits the target and C does not is
A. B. C. D.mediumAsked in NIMCET 2015View solution āŗ - Q25.
In an entrance test there are multiple choice questions, with four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If the student gets the correct answer to a question, then the probability that he was guessing is
A. B. C. D.mediumAsked in NIMCET 2017View solution āŗ - Q26.
A man is known to speak the truth 2 out of 3 times. He throws a die with 1 to 6 on its faces and reports that it is 1. Then the probability that it is actually 1 is
A. B. C. D.mediumAsked in NIMCET 2017View solution āŗ - Q27.
Two persons A and B agree to meet on 20 April 2018 between 6 pm and 7 pm, with the understanding that each will wait no longer than 20 minutes for the other. What is the probability that they meet?
A. B. C. D.mediumAsked in NIMCET 2018View solution āŗ - Q28.
Two numbers a and b are chosen at random from the set of the first 30 natural numbers. The probability that is divisible by 3 is
A. B. C. D.mediumAsked in NIMCET 2019View solution āŗ - Q29.
A committee of 5 is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all is
A. 2/3B. 4/9C. 1/2D. 5/9mediumAsked in NIMCET 2024View solution āŗ - Q30.
If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probability that all three of them are divisible by both 2 and 3 is
A. 4/33B. 4/35C. 4/25D. 4/1155mediumAsked in NIMCET 2024View solution āŗ - Q31.
Let E and F be two events such that and . Which one of the following is NOT equivalent to the condition that ?
A. E and F are independentB. C. D. and F are independentmediumAsked in NIMCET 2025View solution āŗ