I select two cards from a standard deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the followng is an appropriate sample space S for the possible outcomes? A) S = {red, black} B) S = { (red, red), (red, black), (black, red), (black, black) }, where, for example, (red, red) stands for the event "the first card is red and the second card is red." C) S = { (red, red), (red, black), (black, black) }, where, for example, (red, red) stands for the event "the first card is red and the second card is red." D) S = {0, 1, 2}. E) All of the above.

Question

Dangelo Atkinson

Mathematics

4 September, 17:35

I select two cards from a standard deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the followng is an appropriate sample space S for the possible outcomes? A) S = {red, black} B) S = { (red, red), (red, black), (black, red), (black, black) }, where, for example, (red, red) stands for the event "the first card is red and the second card is red." C) S = { (red, red), (red, black), (black, black) }, where, for example, (red, red) stands for the event "the first card is red and the second card is red." D) S = {0, 1, 2}. E) All of the above.

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Answers (1)

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Julian Harvey · Answer 1

B) S = { (red, red), (red, black), (black, red), (black, black) }

See explanation below.

Step-by-step explanation:

Previous concepts

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

Solution to the problem

We know that we have 52 cards. 26 of them red and the other 26 black. And we are going to select two cards at random. We are interested on the correct sampling space. We analyze one by one the options given.

A) S = {red, black}

False. We can obtain two red cards for example or two black cards and these pairs are not included in the sample space provided.

B) S = { (red, red), (red, black), (black, red), (black, black) }, where, for example, (red, red) stands for the event "the first card is red and the second card is red."

True. The cardinality for the sample space is 2^2 = 4 possible outcomes. And as we can see here we have all the possible options included (red, red), (red, black), (black, red), (black, black). So then that's the correct option for the sampling space.

C) S = { (red, red), (red, black), (black, black) }, where, for example, (red, red) stands for the event "the first card is red and the second card is red."

False, the cardinality of the sample space is 2^2 = 4 and on this case the sample space provided have just 3 elements or possible outcomes. We don't have include the possibl option (black, red).

D) S = {0, 1, 2}.

False the sample space are related to red and black cards and we can't have numbers as the possible outcomes for the experiment.

E) All of the above.

False, option B is correct.