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Sample Space

The sample space is the set all possible outcomes.

A fair coin

When flipping a coin alt-text alt-text the sample space is $\left\{\text{Heads, Tails}\right\}$ or $\left\{\text{H, T}\right\}$ abbreviated.
The capital letter is used for sample space.
$n\left(U\right)$ means the number of elements in $U$.
In this example, $n\left(U\right)=$ .

A fair 6-sided die

alt-text

$U=\{$ $\}$ and $n\left(U\right)=$

A deck of cards

alt-text

$U=\{$♦A,♦2,♦3,♦4,♦5,♦6,♦7,♦8,♦9,♦10,♦J,♦Q,♦K,
♣A,♣2,♣3,♣4,♣5,♣6,♣7,♣8,♣9,♣10,♣J,♣Q,♣K,
♥A,♥2,♥3,♥4,♥5,♥6,♥7,♥8,♥9,♥10,♥J,♥Q,♥K,
♠A,♠2,♠3,♠4,♠5,♠6,♠7,♠8,♠9,♠10,♠J,♠Q,♠K$\}$
$n\left(U\right)=$

Other examples

List the sample space for:

The integers from 1 to 5 inclusive.

$U=\{\text{vowels}\}$.

The different ways the letters A, B, and C can be arranged.

$U=\{$ $\}$

$U=\{$ $\}$

$U=\{ABC,ACB,$ $\}$