what is the sample space for this experiment: select two cards from a deck of 52 cards and observe the color of each card drawn.

There are 2 possible colors per card: {red, black}. When drawing 2 cards, there are 4 possibilities for the colors: {red-red, red-black, black-red, black-black}.

To determine the sample space for this experiment, we need to consider all possible outcomes of selecting two cards from a deck of 52 cards and observing the color of each card drawn.

Step 1: Determine the number of options for the first card.
Since there are 52 cards in a deck, there are 52 possibilities for the first card.

Step 2: Determine the number of options for the second card.
Once the first card is drawn, there are only 51 cards remaining for the second card.

Step 3: Determine the number of outcomes for the entire experiment.
Since each card can be either red or black, and we are drawing two cards, there are 2 options for the first card and 2 options for the second card. This gives us a total of 2 x 2 = 4 possible outcomes.

Step 4: List all possible outcomes.
The four possible outcomes are:
1. Red, Red
2. Red, Black
3. Black, Red
4. Black, Black

Thus, the sample space for this experiment is: {Red, Red}, {Red, Black}, {Black, Red}, {Black, Black}.

To determine the sample space for this experiment, we need to consider all the possible outcomes.

In this case, we are selecting two cards from a deck of 52 cards and observing the color of each card drawn.

Step 1: Determine the possible outcomes for the first card.

There are 52 cards in a deck, and each card can either be black or red. So for the first card, the possible outcomes are 52.

Step 2: Determine the possible outcomes for the second card.

After the first card is drawn, there are 51 cards remaining in the deck. The color of the second card drawn can be either black or red, excluding the color of the first card drawn. So for the second card, the possible outcomes are 51.

Step 3: Determine the overall sample space.

To determine the overall sample space, we multiply the number of possible outcomes for the first card (52) by the number of possible outcomes for the second card (51).

Therefore, the sample space for this experiment is 52 × 51 = 2,652 different outcomes. Each outcome represents a pair of cards with their respective colors.