Probability Class 10 Important Questions Last Updated : 11 Jul, 2025 Summarize Comments Improve Suggest changes Share Like Article Like Report Probability is a fundamental concept in mathematics for measuring of chances of an event happening By assigning numerical values to the chances of different outcomes, probability allows us to model, analyze, and predict complex systems and processes.Probability Formulas for Class 10 It says the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes.Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomesFor any event E: P (E) + P ( \bar{E}) = 1, where E stands for ‘not E’P ( \bar{E}) = 1 - P(E) Probability Class 10 Important Questions: Solved Question 1: You toss two coins at the same time. What is the probability of getting at least one head?Solution:The possible outcomes when tossing two coins are: HH, HT, TH, TT (where H = Head, T = Tail).Total possible outcomes = 4.The favorable outcomes for "at least one head" are: HH, HT, TH (3 outcomes).P(at least one head) = number of outcomes with one head / total number of outcomes. P(at least one head) = 3/4Question 2: Two dice are rolled together. What is the probability of getting a sum of 7?Solution:The possible outcomes when rolling two dice = 6×6=36. The favorable outcomes where the sum is 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) (6 outcomes).P(sum of 7) = number of outcomes with sum of 7/ total number of outcomes. P(sum of 7) = 6/36 = 1/6Question 3: A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x. Solution : Total number of balls = 12Number of black Balls = x.P(Getting a black ball ) = number of black Balls / total number of balls. P(Getting a black ball ) = x/12After adding 6 more black balls Total number of balls = 18Number of black Balls = x + 6.Pnew (getting black balls) = x + 6/18Now, Pnew = 2 × POld(x + 6)/18 = 2 × (x/12) (x + 6)/18 = 2x/12 Simplifying the above equationx = 3Question 4: If the probability of winning a game is 0.6, what is the probability of loosing it. Solution: Given the probability of winning the game is 0.6 ⇒ P(E) = 0.6As we know, P (E) + P ( \bar{E}) = 1then probability of loosing the game P ( \bar{E}P ( \bar{E} = 1 - P(E)P(Loosing the game) = 1 - 0.6 = 0.4P(Loosing the game) = 0.4Also Read:ProbabilityProbability TheoryProbability and StatisticsProbability – Aptitude Questions and AnswersProbability Class 10 Important Questions : Unsolved Class 10 : Probability Worksheet with Answers - Free PDF Download Comment More infoAdvertise with us Next Article Mathematics - Law of Total Probability A aniketsingh1 Follow Improve Article Tags : Engineering Mathematics Similar Reads Maths for Machine Learning Mathematics is the foundation of machine learning. Math concepts plays a crucial role in understanding how models learn from data and optimizing their performance. 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In this section, we focus on their use in finding maxima and minima.Note: If f(x) is a continuous function, then for every continuous function on a closed interval has a maximum and a minimum v 6 min read Absolute Minima and MaximaAbsolute Maxima and Minima are the maximum and minimum values of the function defined on a fixed interval. A function in general can have high values or low values as we move along the function. The maximum value of the function in any interval is called the maxima and the minimum value of the funct 11 min read Optimization for Data ScienceFrom a mathematical foundation viewpoint, it can be said that the three pillars for data science that we need to understand quite well are Linear Algebra, Statistics and the third pillar is Optimization which is used pretty much in all data science algorithms. 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