Probability is an important topic in mathematics and quantitative aptitude. It is commonly asked in SSC, banking, railway, state government exams, entrance tests and campus placements. The topic is useful because it checks both concept and calculation speed.
This lesson explains probability in simple language with formulas, shortcut tricks, solved examples, practice questions and FAQs. The goal is to make the topic easy for beginners and useful for exam revision.
What Is Probability?
Probability measures the chance of an event happening. It is written as a number between 0 and 1, where 0 means impossible and 1 means certain.
Important Terms
| Point | Details |
|---|---|
| Experiment | An action with possible outcomes |
| Outcome | A possible result |
| Sample space | Set of all possible outcomes |
| Event | A selected group of outcomes |
| Favourable outcome | Outcome that supports the event |
Important Formulas
| Point | Details |
|---|---|
| Probability | Favourable outcomes / Total outcomes |
| Impossible event | Probability = 0 |
| Certain event | Probability = 1 |
| Complement | P(not A) = 1 – P(A) |
| Equally likely outcomes | All outcomes have same chance |
Step-by-Step Method
- Write total possible outcomes.
- Write favourable outcomes.
- Use probability formula.
- Simplify the fraction.
- Check that answer is between 0 and 1.
Shortcut Tricks
- Coin has 2 outcomes.
- Two coins have 4 outcomes.
- Dice has 6 outcomes.
- Two dice have 36 outcomes.
- A standard deck has 52 cards.
Common Question Types
| Point | Details |
|---|---|
| Coin questions | Head and tail outcomes |
| Dice questions | Numbers 1 to 6 |
| Card questions | 52-card deck |
| Balls in bag | Count favourable balls |
| Complement | Use 1 – probability |
Solved Examples
Example 1
Find probability of head when a coin is tossed.
Favourable = 1, total = 2. Probability = 1/2.
Example 2
Find probability of getting 4 on a die.
Favourable = 1, total = 6. Probability = 1/6.
Example 3
Find probability of even number on a die.
Even outcomes are 2, 4, 6. Probability = 3/6 = 1/2.
Example 4
A bag has 3 red and 2 blue balls. Probability of red?
Favourable = 3, total = 5. Probability = 3/5.
Example 5
Probability of impossible event?
0.
Exam Style Examples
Question 1
Two coins are tossed. Find probability of exactly one head.
Outcomes: HH, HT, TH, TT. Favourable: HT, TH. Probability = 2/4 = 1/2.
List sample space for small cases.
Question 2
A die is thrown. Find probability of number greater than 4.
Favourable outcomes are 5 and 6. Probability = 2/6 = 1/3.
Count outcomes carefully.
Question 3
A card is drawn from 52 cards. Find probability of an ace.
There are 4 aces. Probability = 4/52 = 1/13.
A standard deck has 4 suits and 13 cards in each suit.
Common Mistakes
- Writing favourable outcomes as total outcomes.
- Giving probability greater than 1.
- Forgetting to simplify fraction.
- Confusing at least one with exactly one.
- Using 6 outcomes for two dice instead of 36.
Practice Questions
- Probability of tail in one coin toss.
- Probability of odd number on a die.
- Probability of prime number on a die.
- Probability of red ball from 4 red and 6 blue balls.
- Probability of king from a deck.
- Probability of not getting head in coin toss.
- Probability of number less than 5 on die.
- Probability of getting 7 on normal die.
- Probability of certain event.
- Probability of black card from deck.
Answers to Practice Questions
- 1/2
- 1/2
- 1/2
- 2/5
- 1/13
- 1/2
- 2/3
- 0
- 1
- 1/2
Frequently Asked Questions
What is probability?
It is the measure of chance of an event.
What is probability formula?
Probability = favourable outcomes / total outcomes.
Can probability be more than 1?
No, probability is always between 0 and 1.
What is sample space?
It is the set of all possible outcomes.
How many outcomes are there for two dice?
There are 36 outcomes.
Revision Notes
Probability is counting favourable outcomes out of total outcomes. Always check total cases first.
Revise the main formula and then solve at least five direct questions. After that, solve mixed word problems. This order gives better clarity and speed.
Conclusion
Probability becomes easy when sample space and favourable outcomes are counted correctly.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.
Additional Exam Practice Note
In Probability, most questions follow fixed patterns. Read the condition carefully and convert it into a formula. If two actions happen together, combine their rates or cases properly. If the question asks for probability, count favourable and total outcomes. If the question asks for tank filling or emptying, treat filling as positive and emptying as negative.
Students should practise easy questions first and then move to mixed examples. Timed practice is helpful only after the concept is clear. Accuracy should come before speed.
Before final answer, check whether the value is possible. A probability must be between 0 and 1. A tank filling time must be positive. Such checks reduce mistakes in exams.