Shuffle a deck of cards and turn over the first card. what is the sample space of the experiment? how many outcomes are in the event that the first card is a heart?

The sample space contain 52 entities as shown in explanation.

The event that first card is a heart, contains 13 outcomes as shown in the explanation.

Explanation:

The sample space will contain 52 entities as follows:

Sample Space = {Heart 1, Heart 2,Heart 3,Heart 4,Heart 5,Heart 6,Heart 7,Heart 8,Heart 9,Heart Jack,Heart Queen, Heart King,Heart A,Spade 1, Spade 2,Spade 3,Spade 4,Spade 5,Spade 6,Spade 7,Spade 8,Spade 9,Spade Jack,Spade Queen, Spade King,Spade A, Diamond 1, Diamond 2,Diamond 3,Diamond 4,Diamond 5,Diamond 6,Diamond 7,Diamond 8,Diamond 9,Diamond Jack,Diamond Queen, Diamond King,Diamond A, Club 1, Club 2,Club 3,Club 4,Club 5,Club 6,Club 7,Club 8,Club 9,Club Jack,Club Queen, Club King,Club A}

There will be 13 outcomes in the event that first card is a heart, as follows:

Event(first card hearts) = {Heart 1, Heart 2,Heart 3,Heart 4,Heart 5,Heart 6,Heart 7,Heart 8,Heart 9,Heart Jack,Heart Queen, Heart King,Heart A}