- #1

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## Homework Statement

A card is drawn at random from an ordinary deck of 52 playing cards (which means there are 0 jokers).

Give the sample space.

## Homework Equations

A set that consists of all possible outcomes of a random experiment is called a sample space, and each possible outcome of the aforementioned random experiment is called a sample point.

## The Attempt at a Solution

__My confusion:__

Is

S = {A♥, A♠, A♦, A♣, 2♥, 2♠, 2♦, 2♣, 3♥, 3♠, 3♦, 3♣, 4♥, 4♠, 4♦, 4♣, 5♥, 5♠, 5♦, 5♣, 6♥, 6♠, 6♦, 6♣, 7♥, 7♠, 7♦, 7♣, 8♥, 8♠, 8♦, 8♣, 9♥, 9♠, 9♦, 9♣, 10♥, 10♠, 10♦, 10♣, J♥, J♠, J♦, J♣, Q♥, Q♠, Q♦, Q♣, K♥, K♠, K♦, K♣}

the only way to describe the sample space (ignoring order of the elements, since a set with the same exact elements but in a different order are equal), or not?

Is it possible to give another set S_2 that consists of unordered pairs such as what is shown below?:

S_2 = {(A,♥), (A,♠), (A,♦), (A,♣), (2,♥), (2,♠), (2,♦), (2,♣), (3,♥), (3,♠), (3,♦), (3,♣), (4,♥), (4,♠), (4,♦), (4,♣), (5,♥), (5,♠), (5,♦), (5,♣), (6,♥), (6,♠), (6,♦), (6,♣), (7,♥), (7,♠), (7,♦), (7,♣), (8,♥), (8,♠), (8,♦), (8,♣), (9,♥), (9,♠), (9,♦), (9,♣), (10,♥), (10,♠), (10,♦), (10,♣), (J,♥), (J,♠), (J,♦), (J,♣), (Q,♥), (Q,♠), (Q,♦), (Q,♣), (K,♥), (K,♠), (K,♦), (K,♣)}

Assuming everything I said up until now is correct, are A♥ and (A,♠) each a (correct/valid) sample point?

In short, I want to ask if the set can be a "regular" set with one element at a time, or if it can also be a set of unordered pairs (such as the above set S_2, where the ordering of the pairs and the ordering of the elements in the pairs both do not matter - because that is what it means to be a set with unordered pairs)?

Any input would be GREATLY appreciated!