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Sample Spaces

Okayama Castle_102922A
[Okayama Castle, Japan]

- Overview

There are three main types of sample spaces: finite, countably infinite, and uncountably infinite.

  • Finite sample space: This type contains a limited, countable number of outcomes. For example, when flipping a coin, the outcomes (heads, tails) are finite.
  • Countably infinite sample space: This type has an infinite number of outcomes, but they can be put into a one-to-one correspondence with the set of natural numbers (1, 2, 3, ...). For example, the number of defective products in a batch can be infinite, but you can still count them (1, 2, 3, ...).
  • Uncountably infinite sample space: This type also has an infinite number of outcomes, but they cannot be put into a one-to-one correspondence with the natural numbers. For example, the range of possible heights of a person is uncountably infinite.

 

Please refer to the following for more information:

 

- Finite Sample Spaces

A finite sample space is a sample space (the set of all possible outcomes of a random experiment) that contains a limited or countable number of outcomes. Examples include flipping a coin, rolling a die, or drawing a card from a deck. In contrast, an infinite sample space contains an unlimited number of outcomes, such as measuring the time until an event occurs. 

Key characteristics of finite sample spaces:

  • Countable: The number of possible outcomes is finite and can be counted.
  • Discrete: Often associated with discrete probabilities, where outcomes can be listed or counted.
  • Simpler: Finite sample spaces are generally easier to understand and work with mathematically compared to infinite sample spaces.

 

- Examples of Finite Sample Spaces

  • Coin flip: The sample space is {Heads, Tails}.
  • Rolling a six-sided die: The sample space is {1, 2, 3, 4, 5, 6}.
  • Drawing a card from a standard deck: The sample space contains 52 possible outcomes (cards).
  • Choosing a birthday: The sample space is the set of all possible dates in a given year.
  • Tossing two coins: The sample space is {HH, HT, TH, TT}.
  • Rolling two dice: The sample space is a set of 36 possible outcomes (pairs of numbers from 1 to 6). 

 

[More to come ...]



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