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In most examination questions Method 2 above is easier to apply and is therefore preferred.
MathsNet imageBlaise Pascal (June 19, 1623 – August 19, 1662), mathematician and philosopher, was educated at home by his father, himself a considerable mathematician. The origins of probability are usually found in the correspondence between Pascal and Fermat where they treated several problems associated with games of chance. The letters were not published but their contents were known in Parisian scientific circles. Pascal's only probability publication was the posthumously published Traite du triangle arithmetique (1654); this treated Pascal's triangle with probability applications. Pascal introduced the concept of expectation and discussed the problem of gambler's ruin.

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of a random variable X and denoted by E(X), where E(X) = sum of all values of x.P(X=x).

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This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)S1ProbabilityTheoretical-
AQA A2 Maths 2017StatisticsProbabilityConditional Probability-
AQA AS/A2 Maths 2017StatisticsProbabilityConditional Probability-
CBSE XII (India)ProbabilityProbabilityTotal probability-
CBSE XI (India)Statistics and ProbabilityProbabilityProbability of 'not ,'and', 'or' events-
CCEA A-Level (NI)S1ProbabilityTheoretical-
CIE A-Level (UK)S1ProbabilityTheoretical-
Edexcel A-Level (UK - Pre-2017)S1ProbabilityTheoretical-
Edexcel A2 Maths 2017StatisticsConditional ProbabilityConditional Probability-
Edexcel AS/A2 Maths 2017StatisticsConditional ProbabilityConditional Probability-
I.B. Higher Level5ProbabilityTheoretical-
I.B. Standard Level5ProbabilityTheoretical-
Methods (UK)M15ProbabilityTheoretical-
I.B. (MSSL)3ProbabilityTheoretical-
OCR A-Level (UK - Pre-2017)S4ProbabilityTheoretical-
OCR A2 Maths 2017StatisticsConditional ProbabilityConditional Probability-
OCR MEI A2 Maths 2017StatisticsConditional ProbabilityConditional Probability-
OCR-MEI A-Level (UK - Pre-2017)S1ProbabilityTheoretical-
Pre-Calculus (US)E4ProbabilityTheoretical-
Pre-U A-Level (UK)ProbProbabilityTheoretical-
Scottish (Highers + Advanced)HSProbabilityTheoretical-
Scottish HighersSProbabilityTheoretical-
Universal (all site questions)PProbabilityTheoretical-
WJEC A-Level (Wales)S1ProbabilityTheoretical-