ProbabilityTutorial 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 ProbabilityRandomnessIn 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 experimentTrialA 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 ProbabilityIndependent TrialSuccessive 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.ExperimentExperiment 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 ProbabilityEventAn event is a possible outcome of the Experiment. Like head coming in a toss

Sample spaceIt 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

Empirical Probability1) If the event A, B, C covers the entire possible outcome in the experiment. Then,P (A) +P (B) +P(C) =12) The probability of an event (U) which is impossible to occur is 0. Such an event is called an impossible eventP (U)=03) 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 eventP(X) =14) Probability of any event can be as0≤ P(E) ≤1

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