A standard deck of cards has 52 cards. The cards have one of two colors: 26 cards in the deck are red and 26 are black. The cards have one of four denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). One card is selected at random and the denomination is recorded. What is the sample space S for the set of possible outcomes?

Question

Gia Perkins

Mathematics

18 July, 03:14

A standard deck of cards has 52 cards. The cards have one of two colors: 26 cards in the deck are red and 26 are black. The cards have one of four denominations: 13 cards are hearts (red), 13 cards are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black). One card is selected at random and the denomination is recorded. What is the sample space S for the set of possible outcomes?

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Terrance Mcconnell · Answer 1

S={ (heart), (diamond), (club), (spade) }

Step-by-step explanation:

In probability, a set is a well-defined collection of objects, product of an independent successful operation.

A sample space is the combination of all possible outcomes in an operation, so in this case, when we select one card and record the denomination, then we need to check what characteristic from the card are we looking for, from the problem we can see that is the denomination by itself, not the color, the number of the card, or anything else, and we only have 4 options of denomination so the sample space would be:

S={ (heart), (diamond), (club), (spade) }