Probability

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Probability is the numerical measure of the likelihood of an event occurring. It quantifies words like 'probably', 'likely', 'possibly' into numbers between 0 and 1. For example, if a coin is tossed 1…

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Experimental probability is based on the results of actual experiments. Formula: P(E) = Number of trials in which the event happened / Total number of trials. Example: If you toss a coin 100 times and…

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Theoretical probability assumes equally likely outcomes and is calculated without performing experiments. Formula: P(T) = Number of outcomes favourable to T / Number of all possible outcomes of the ex…

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Outcomes are equally likely when chances of getting them are equal. Examples: (1) Getting digits 1,2,3,4,5,6 when rolling a fair dice - each has probability 1/6, (2) Selecting any card from a well-shu…

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Sample space is the set of all possible outcomes of an experiment. Examples: (1) Tossing a coin: S = {H, T}, (2) Rolling a dice: S = {1, 2, 3, 4, 5, 6}, (3) Drawing a ball from bag with red, blue, yel…

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Two or more events are mutually exclusive if occurrence of one event prevents occurrence of all other events. Examples: (1) Getting head or tail in a coin toss - both cannot occur together, (2) A stud…

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Sample space S = {1, 2, 3, 4, 5, 6}, so n(S) = 6. Prime numbers on a dice are {2, 3, 5}, so n(E) = 3. Using formula P(E) = n(E)/n(S), P(prime number) = 3/6 = 1/2. Therefore, probability is 1/2 or 0.5.

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An elementary event has only one outcome in an experiment. Examples: Getting exactly 3 on a dice, getting heads in coin toss. Special property: The sum of probabilities of all elementary events in an …