- #1

- 805

- 8

## 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!