The document discusses probability and sample spaces. It defines a sample space as the set of all possible outcomes, such as the numbers 1 through 6, which would have a sample space size of 6. It provides a formula for calculating probability as the number of favorable outcomes divided by the total number of possible outcomes. Probability values range from 0, meaning an event will never occur, to 1, meaning an event is certain to occur. Two short examples are given to illustrate applying the probability formula.

1. ProbabilityMathematics Chapter 12

2. Sample spaceIf the possible outcomes are 1, 2, 3, 4, 5 and 6, S = {1, 2, 3, 4, 5, 6}, where S is sample space or the possible outcomes.In this example, the number of possible outcomes or elements in the sample space is 6 and is denoted by n(S) = 6.If S = {5, 6, 7, 8, … , 32, 33, 34, 35}, then n(S) = 35 – 5 + 1 = 31.

3. Formula of ProbabilityThe probability of an event is denoted as P(E).P(E) = = For ExampleP(E) = = =When P(E) is 0, the event will never happen.When P(E) is 1, the event will definitely happen. Number of Favourable Outcomes for event n(E) Total Number of Outcomes n(S)Even numbers from 1 to 10 5 1Integers from 1 to 10 10 2

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