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.Which of the following is the correct sample space S for the set of possible outcomes?
A)S = {red,black}
B)S = {red,red,black,black}
C)S = {hearts,diamonds,clubs,spades}
D)S = {red,black,hearts,diamonds,clubs,spades}

Question

Quizplus · Accepted Answer

The sample space S should represent all possible outcomes of selecting a card in terms of its denomination. Therefore, option A is incorrect as it only considers the color. Option B is incorrect as it lists duplicate outcomes. Option D is incorrect as it combines both color and denomination which may lead to confusion. Option C is correct as it lists all four possible denominations in the deck.

A Standard Deck of Cards Has 52 Cards