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 speaks the truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating some incident is
A. 1/4B. 1/3C. 1/2D. 2/3easyAsked in NIMCET 2024View solution › - Q22.
Let A and B be two events defined on a sample space . Suppose denotes the complement of A relative to the sample space . Then the probability equals
A. B. C. D.easyAsked in NIMCET 2024View solution › - Q23.
Region R is defined as the region in the first quadrant satisfying the condition . Given that a point lies in R, what is the probability that ?
A. 1B. 0C. 1/2D. 1/3easyAsked in NIMCET 2024View solution › - Q24.
The captains of five cricket teams, including India and Australia, are lined up randomly next to one another for a group photo. What is the probability that the captains of India and Australia will stand next to each other?
A. B. C. D.easyAsked in NIMCET 2025View solution › - Q25.
There are two coins, say blue and red. For the blue coin, the probability of getting a head is 0.99 and for the red coin, it is 0.01. One coin is chosen randomly and is tossed. The probability of getting a head is
A. 0.02B. 0.5C. 1D. 0.98easyAsked in NIMCET 2025View solution › - Q26.
In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
A. B. C. D.easyAsked in NIMCET 2025View solution ›