Probability – Important Formulas & Notes
Numerical Aptitude Notes for APSC Prelims CSAT Paper, SSC and Competitive Exams
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Probability
A quantitative measure of the chance of occurrence of a particular event. The likelihood of the occurrence of a particular event. The probability of event A is often written as P(A).
The probability of an event can only be between 0 and 1 and can also be written as a percentage.
Probability of Occurrence of an Event
Let S be the sample and let E be an event.
P(E) = n(E) /n(S)
Results on Probability
P(S) = 1
0 <= P (E) <= 1
P(
) = 0
For any events A and B, P(A 
B) = P(A) + P(B) – P(A 
B)
Experiment – An operation which can produce some well-defined outcomes is called an experiment.
Random Experiment – An experiment in which all possible outcomes are know and the exact output cannot be predicted in advance, is called a random experiment. Like drawing a card from a pack of well-shuffled cards.
Sample Space – When we perform an experiment, then the set S of all possible outcomes is called the sample space.
In tossing a coin, S = {H, T}
If two coins are tossed, S = {HH, HT, TH, TT}.
In rolling a dice, S = {1, 2, 3, 4, 5, 6}.
Event – Any subset of a sample space is called an event.
Equally Likely Events – Events are said to be equally likely if there is no preference for a particular event over the other.
Mutually Exclusive Events – Two or more than two events are mutually exclusive if the occurrence of one of the events excludes the occurrence of the other.
Independent Events – If the occurrence or non-occurrence of one event does not influence the occurrence or non-occurrence of the other.
Simple Events – Events where one experiment happens at a time and it has a single outcome.
Compound Event – An event in which there is more than one possible outcome.
Exhaustive Events – The mutually exclusive events that form the sample space collectively are called the exhaustive events. Example, when a coin is tossed, either Head or Tail appears and they collectively form the sample space.