There are 52 cards in a standard deck of cards, with four suites: hearts, clubs, diamonds and spades. Each suit has 13 cards: Ace, $$ 2,3,4,5,6,7,8,9,10 $$, Jack, Queen, King . Let event $$ A $$ be choosing a card with 7 out of a standard deck of cards. Identify the numbers of each of the following. Enter the probability as a fraction: Provide your answer below: There are $$ \square $$ cards in the sample space. There are $$ \square $$ cards in event A. $$ \mathrm{P}(\mathrm{A})=\square $$, is the probability that you choose a 7 out of the deck of cards.

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In a standard deck of 52 cards, we can analyze the situation as follows:

1. **Sample Space**: The total number of cards in the sample space is 52.

$$
   \text{Number of cards in the sample space} = 52
   $$

2. **Event A**: The event $$ A $$ is choosing a card with 7. There are four 7s in the deck (7 of hearts, 7 of clubs, 7 of diamonds, and 7 of spades).

$$
   \text{Number of cards in event A} = 4
   $$

3. **Probability of Event A**: The probability $$ P(A) $$ is calculated as the number of favorable outcomes (cards that are 7) divided by the total number of outcomes (total cards in the deck).

$$
   P(A) = \frac{\text{Number of cards in event A}}{\text{Number of cards in the sample space}} = \frac{4}{52} = \frac{1}{13}
   $$

Putting it all together, we have:

- There are $$ 52 $$ cards in the sample space.
- There are $$ 4 $$ cards in event A.
- $$ P(A) = \frac{1}{13} $$.

So the final answers are:

- Sample space: $$ 52 $$
- Event A: $$ 4 $$
- Probability $$ P(A) = \frac{1}{13} $$
There are 52 cards in the sample space. There are 4 cards in event A. $$ P(A) = \frac{1}{13} $$.

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