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What is probability

This document provides an overview of key concepts in probability. It defines probability as a measure of likelihood between 0 and 1, and discusses how probability is used in various fields. Key terms are explained, such as randomness, trial, independent trial, experiment, event, and sample space. Randomness refers to experiments with unpredictable outcomes, like rolling a die. Trials are the individual occurrences of an experiment, like each coin toss. The document also discusses empirical probability, which is the probability of an event calculated based on the frequency of outcomes from experiments. Empirical probability depends on the specific experiment and can take on different values.

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Probability Tutorial on Probability Class 9
What is probability • Probability is the measure of the likeliness that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty) • It is widely used in the study of Mathematics, Statistics, Gambling, Physical sciences, Biological sciences, Weather forecasting, Finance etc. to draw conclusions. Insurance companies uses this to decide on financial policies
Terms in Probability Randomness In mathematics, When next outcome of the experiment can not be determined then we say it is a random experiment e.g. Consider the dice. When we throw the dice, we cannot determine what number will come Since we cannot predict the next outcome, we may say it is a random experiment Trial A trial is an action which results in one or several outcomes, for example each toss of the coin and each throw of the die are called trials
Terms in Probability Independent Trial Successive trials of some random event for example tosses of a coin, throws of a die are said to be independent if the outcome of any one trial does not impact the outcomes of any others. Experiment Experiment and trial are same thing as such. An experiment is a situation involving chance or probability that leads to results called outcomes. But sometimes we use experiment to refer to whole large number of trials.
Terms in Probability Event An event is a possible outcome of the Experiment. Like head coming in a toss Sample space It is a set of all possible outcomes of an experiment. e.g. when we coin is tossed, the possible outcome are Head and Tail. So sample space is Head and tail
Empirical Probability 1) Experimental or empirical probability is an estimate that an event will happen based on how often the event occurs after performing an experiment in a large number of trials. 2) It is a probability of event which is calculated based on experiments 3) Empirical probability depends on experiment and different will get different values based on the experiment
Empirical Probability 1) If the event A, B, C covers the entire possible outcome in the experiment. Then, P (A) +P (B) +P(C) =1 2) The probability of an event (U) which is impossible to occur is 0. Such an event is called an impossible event P (U)=0 3) The probability of an event (X) which is sure (or certain) to occur is 1. Such an event is called a sure event or a certain event P(X) =1 4) Probability of any event can be as 0≤ P(E) ≤1
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