Probability

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A random experiment is an operation which gives some outcomes (results) under given conditions, but we cannot predict the exact outcome beforehand. Examples: tossing a coin, throwing a die, drawing a …

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Sample space is the set of all possible outcomes of a random experiment. It is denoted by S. Example: When tossing a coin, S = {H, T}. When throwing a die, S = {1, 2, 3, 4, 5, 6}.

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An event is any outcome or combination of outcomes of a random experiment. It is a subset of the sample space. Example: When throwing a die with S = {1, 2, 3, 4, 5, 6}, getting an even number is an ev…

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A simple event (or elementary event) is an event that contains only one element from the sample space. It is a singleton set. Example: When tossing a coin, getting a head {H} is a simple event.

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P(E) = Number of favorable outcomes / Total number of possible outcomes where P(E) is the probability of event E occurring.

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The probability of any event always lies between 0 and 1, inclusive. 0 ≤ P(E) ≤ 1 When P(E) = 0, it's an impossible event. When P(E) = 1, it's a sure event.

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Sample space S = {H, T} Favorable outcomes = {H} Number of favorable outcomes = 1 Total outcomes = 2 P(getting head) = 1/2 = 0.5…

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Sample space S = {1, 2, 3, 4, 5, 6} Event E = getting even number = {2, 4, 6} Favorable outcomes = 3 Total outcomes = 6 P(E) = 3/6 = 1/2…