Find the sample space for the experiment.

You toss a coin and a six-sided die.

For the first case we are going to assume that the order matters, on this case 6, H is not the same as H, 6

The sampling space denoted by S and is given by:

S = { (1, H), (2, H), (3, H), (4, H), (5, H), (6, H),

(1, T), (2, T), (3, T), (4, T), (5, T), (6, T),

(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6),

(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) }

If we consider that (5, H) is equal to (H, 5) "order no matter" then we will have just 12 elements in the sampling space:

S = { (1, H), (2, H), (3, H), (4, H), (5, H), (6, H),

(1, T), (2, T), (3, T), (4, T), (5, T), (6, T) }

Step-by-step explanation:

By definition the sample space of an experiment "is the set of all possible outcomes or results of that experiment".

For the case described here: "Toss a coin and a six-sided die".

Assuming that we have a six sided die with possible values {1,2,3,4,5,6}

And for the coin we assume that the possible outcomes are {H, T}

For the first case we are going to assume that the order matters, on this case 6, H is not the same as H, 6

The sampling space denoted by S and is given by:

S = { (1, H), (2, H), (3, H), (4, H), (5, H), (6, H),

(1, T), (2, T), (3, T), (4, T), (5, T), (6, T),

(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6),

(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6) }

If we consider that (5, H) is equal to (H, 5) "order no matter" then we will have just 12 elements in the sampling space:

S = { (1, H), (2, H), (3, H), (4, H), (5, H), (6, H),

(1, T), (2, T), (3, T), (4, T), (5, T), (6, T) }