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).Two cards are selected at random and the color 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), (red,black), (black,red), (black,black)}
C)S = {0,1,2}
D)S = {red,black,hearts,diamonds,clubs,spades}

Question

Quizplus · Accepted Answer

The sample space consists of all possible outcomes when two cards are selected at random. Each outcome is represented by a pair of colors (red or black) chosen without replacement. Therefore, the correct sample space is {(red,red), (red,black), (black,red), (black,black)}. Option A only lists the possible colors and not the pairs, Option C and D are incorrect because they include outcomes that are not possible (i.e. selecting 0 or 1 cards, or specifying a suit instead of a color).

A Standard Deck of Cards Has 52 Cards