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The set of all possible outcomes is known as __________.
Question

The set of all possible outcomes is known as __________.

A.

null set

B.

event

C.

sample space

D.

probability

Correct option is C

1. The sample space, denoted by S or Ω, is the set of all possible outcomes of a random experiment. Example: Tossing a coin S={Heads,Tails} Rolling a die S={1,2,3,4,5,6}2. Each individual outcome in the sample space is called a sample point.3. An event is a subset of the sample space.4. If all outcomes in S are equally likely, it’s called a uniform sample space.5. In probability theory:P(E)=Number of favorable outcomesTotal outcomes in sample space6. Used in statistics, probability, and random process modeling — critical in engineering reliabilityrisk analysissimulation, etc.\begin{aligned}&\textbf{1.} \ \text{The \textit{sample space}, denoted by } S \text{ or } \Omega, \text{ is the set of all possible outcomes of a random experiment.} \\&\quad \bullet \ \text{Example: Tossing a coin } \rightarrow S = \{\text{Heads}, \text{Tails}\} \\&\quad \bullet \ \text{Rolling a die } \rightarrow S = \{1, 2, 3, 4, 5, 6\} \\\\&\textbf{2.} \ \text{Each individual outcome in the sample space is called a \textit{sample point}.} \\\\&\textbf{3.} \ \text{An \textit{event} is a \textit{subset} of the sample space.} \\\\&\textbf{4.} \ \text{If all outcomes in } S \text{ are equally likely, it's called a \textit{uniform sample space}.} \\\\&\textbf{5.} \ \text{In probability theory:} \\&P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes in sample space}} \\\\&\textbf{6.} \ \text{Used in statistics, probability, and random process modeling — critical in \textbf{engineering reliability}, \textbf{risk analysis}, \textbf{simulation}, etc.}\end{aligned}​​

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