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Probability

Probability is a branch of mathematics that measures the likelihood or chance of a specific event occurring during a random experiment. In Class 10, the focus is on theoretical probability, which assumes that all possible outcomes of an experiment are equally likely. The probability of an event always lies between 0 and 1, inclusive.

Key Concepts

An event with a probability of 0 is called an impossible event, while an event with a probability of 1 is called a sure or certain event.
The sum of the probabilities of all the elementary events of an experiment is always equal to 1.
For any event E, the probability of the event occurring and the probability of the event not occurring (complementary event) always add up to 1.

Formula & Equation

P(E)=Number of outcomes favourable to ENumber of all possible outcomes of the experimentP(E) = \frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of the experiment}}

P(E) represents the theoretical probability of event E occurring.

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Common Misconceptions

Myth: A probability can be a negative number or greater than 1, such as 1.5 or 150 percent.
Fact: The probability of any event is always a fraction or decimal ranging from 0 to 1. It can never be negative or exceed 1.

Real World Applications

Tossing a fair coin to decide which team gets to bat first in a cricket match, as the outcomes (heads or tails) are equally likely.
Drawing a specific card, like an Ace, from a well-shuffled standard deck of 52 playing cards to determine the winner of a game.

Frequently Asked Questions

What is the difference between theoretical and empirical probability?
Empirical probability is based on the actual results of an experiment conducted multiple times, whereas theoretical probability predicts the likelihood of an event based on mathematical reasoning and equally likely outcomes.
What is a complementary event in probability?
A complementary event represents all outcomes where the specific event does not happen. The sum of the probability of an event and its complementary event is always 1.

Keep Learning

Theoretical ProbabilityEqually Likely OutcomeComplementary Event