PROBABILITY
Frequently Asked Questions
Probability is a numerical measure of the likelihood of an event occurring when the outcome of an experiment is uncertain.
Classical probability is defined as the ratio of the number of favourable outcomes to the total number of equally likely outcomes.
\( P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of equally likely outcomes}} \)
A random experiment is an activity that produces one outcome from several possible outcomes, where the exact result cannot be predicted in advance.
The sample space is the complete set of all possible outcomes of a random experiment.
An event is a specific outcome or a collection of outcomes from the sample space.
Outcomes are equally likely if each outcome has the same chance of occurring.
A sure event is an event that always occurs when the experiment is performed.
The probability of a sure event is 1.
An impossible event is one that cannot occur under any circumstance in the experiment.
The probability of an impossible event is 0.
The value of probability always lies between 0 and 1, inclusive.
No, probability can never be negative.
No, probability cannot exceed 1.
The complement of an event consists of all outcomes that are not part of the event.
\( P(\overline{E}) = 1 - P(E) \)
They simplify probability calculations when finding the probability of an event is difficult directly.
Theoretical probability is calculated using logical reasoning without performing actual experiments.
No, only theoretical (classical) probability is included in the NCERT Class X syllabus.
Tossing a coin, rolling a die, or drawing a card from a deck are common examples.
There are six possible outcomes: 1, 2, 3, 4, 5, and 6.
There are three even numbers out of six outcomes, so the probability is \( \frac{3}{6} = \frac{1}{2} \).
A simple event consists of only one outcome from the sample space.
A compound event consists of two or more outcomes combined together.
Incorrect counting leads to wrong probability values even if the formula is correct.
Listing outcomes helps in visualising the sample space clearly and avoiding omissions.
Yes, probability is usually expressed as a fraction or a decimal between 0 and 1.
Probability helps in predicting chances in games, weather forecasting, insurance, and decision-making under uncertainty.
Fairness means that all outcomes have equal chances of occurring.
The classical probability formula cannot be directly applied.
To maintain conceptual clarity and avoid advanced statistical complexity at the school level.
Favourable outcomes are those outcomes that satisfy the condition of the given event.
Probability is based on logical analysis of chance, not guessing.
There is one favourable outcome out of two, so the probability is \( \frac{1}{2} \).
Such an outcome is impossible, so the probability is 0.
Errors in sample space formation and incorrect counting of outcomes are common mistakes.
Answers should include the formula, correct substitution, simplification, and final result.
It forms the foundation for advanced topics in statistics and data analysis.
Probability develops logical reasoning, analytical thinking, and decision-making skills.
Understanding how to quantify uncertainty using logical and mathematical reasoning.
No, in Class X probability values are rational numbers derived from counting outcomes.
Probability measures uncertainty, while certainty implies a guaranteed outcome.
The probability of the entire sample space is always 1.
To build a conceptual base for statistics, economics, science, and data interpretation.
By carefully defining the sample space and systematically counting outcomes.
