Probability Online Practice Worksheet

Class 10 Probability – Complete Online Practice Guide

Probability is the mathematical way of measuring how likely an event is to happen. Class 10 students use probability to describe outcomes of experiments such as tossing coins, rolling dice, drawing cards, selecting objects and choosing numbers. This DigiSadhan online worksheet is designed for repeated practice: students can choose the number of questions, select a question type and difficulty, start a timed test, check each response and review the solution only after checking.

1. Understanding an Experiment and Outcomes

An experiment is an action or process whose result can be observed. Tossing a coin, rolling a die and selecting one ball from a bag are common probability experiments. Each possible result is called an outcome. The collection of all possible outcomes is called the sample space. For example, when a coin is tossed once, the sample space contains Head and Tail. When a standard die is rolled, the possible outcomes are 1, 2, 3, 4, 5 and 6.

2. Equally Likely Outcomes

Outcomes are equally likely when each outcome has the same chance of occurring. A fair coin gives Head and Tail equally likely chances. A fair die gives each of its six faces an equal chance. Many school-level probability questions are built around this idea, so students should first identify the sample space and then count the favourable outcomes.

3. Probability of an Event

An event is a collection of one or more outcomes. If a die is rolled and the event is “getting an even number,” the favourable outcomes are 2, 4 and 6. There are three favourable outcomes out of six possible outcomes. The probability is therefore 3/6, which can be simplified to 1/2. Always reduce fractions where appropriate and read the wording carefully before counting.

4. Range of Probability

A probability cannot be negative and cannot be greater than 1. A probability of 0 represents an impossible event, while a probability of 1 represents a certain event. Values between 0 and 1 represent different levels of likelihood. This simple range is also a useful way to check an answer: if your calculated probability is below 0 or above 1, something in the counting or calculation needs to be corrected.

5. Complementary Events

The complement of an event E means that E does not occur. If an event has probability P(E), its complement has probability 1 − P(E). For example, if the probability of getting a six on a die is 1/6, the probability of not getting a six is 5/6.

6. Coins, Dice and Cards

Coin questions require careful counting of the possible sequences when more than one coin is tossed. For two coins, the equally likely ordered outcomes are HH, HT, TH and TT. Dice questions commonly ask about even numbers, odd numbers, multiples, primes, sums or particular values. Card questions require attention to the standard 52-card pack and the exact wording of the event, such as a heart, a king, a red card or a particular suit.

7. Drawing Objects from a Collection

Questions involving coloured balls, marbles, tokens or slips are solved by counting the total number of objects and then counting how many satisfy the required condition. If the question says that one object is selected at random and every object is equally likely to be selected, the standard probability formula can be applied directly.

8. How to Solve Probability Questions

First, identify the experiment. Second, write or mentally determine the sample space. Third, identify the favourable outcomes. Fourth, apply the probability formula. Finally, simplify the fraction and check that the answer lies between 0 and 1. For word problems, underline words such as “not,” “at least,” “even,” “odd,” “prime,” “red,” “multiple,” and “without” because they can change the required event.

9. Smart Practice Strategy

Start with Easy questions to build accuracy, move to Medium questions for concept practice, and use Hard questions for exam-level challenge. Do not reveal a solution before attempting a question. Instead, enter your answer and press Check Answer. A correct response turns green and a wrong response turns red. The solution button then becomes available. This encourages active recall rather than copying an answer.

10. Using the DigiSadhan Worksheet

Choose 10 to 2,000 questions, select a category or Mixed mode, choose difficulty and optionally set a timer. Press Start New Test. The worksheet creates a fresh randomized set. Use Shuffle Whole Worksheet whenever you want another fresh set. The progress bar shows attempted questions, while the score counter updates after checked answers. Sound feedback can be switched off when silent study is preferred.

11. Exam Preparation Tips

For examinations, practise both direct formula questions and application-based questions. Learn the meaning of sample space, event, favourable outcome and complementary event. Check every fraction carefully. Avoid assuming outcomes are equally likely unless the question or experiment supports that assumption. With repeated timed practice, students can improve calculation speed while also developing the habit of writing a logical probability setup before calculating.

12. Key Formula Revision

This online worksheet is a practice resource for Class 10 Mathematics students. It is designed to make Probability revision interactive, mobile-friendly and repeatable. Students should use their prescribed textbook and teacher guidance for the complete syllabus and examination requirements.