Probability

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A random experiment is a process by which we observe something uncertain that has more than one possible outcome and the outcome cannot be predicted in advance. Example: Rolling a die - we cannot pred…

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Sample space is the set of all possible outcomes of a random experiment. For tossing two coins: S = {HH, HT, TH, TT} where H = Head and T = Tail.

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An event is a subset of the sample space. It represents a collection of one or more outcomes from a random experiment. For example, if we roll a die and want 'even numbers', the event E = {2, 4, 6} wh…

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P(E) = Number of Favourable Outcomes / Total Number of Outcomes. This formula applies when all outcomes are equally likely to occur. The probability value ranges from 0 to 1.

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Two events are mutually exclusive if the occurrence of one rules out the occurrence of the other. Mathematically, E ∩ F = ∅. Example: When rolling a die, getting an even number and getting an odd numb…

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Independent events: The probability of one event is unaffected by the occurrence of another. Example: Tossing two coins - result of first coin doesn't affect second. Dependent events: The probability …

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Impossible event: An event that cannot occur, represented by empty set ∅, P(impossible) = 0. Example: Getting 7 on a standard die. Sure event: An event that must occur, represented by sample space S, …

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A set of events is exhaustive if all events together consume the entire sample space. Their union equals the sample space. Example: When rolling a die, events E₁ = {1,2,3} and E₂ = {4,5,6} are exhaust…