To determine the probability of drawing a red 10 from a deck of 52 cards, let's break down the problem step by step.
1. Understand the composition of a standard deck:
- A standard deck has 52 cards.
- These 52 cards are divided into 4 suits: Hearts, Diamonds, Clubs, and Spades.
- Each suit has 13 cards: Ace through 10, Jack, Queen, and King.
2. Identify the red suits:
- The red suits in a deck are Hearts and Diamonds.
3. Determine the number of 10s in the red suits:
- Each red suit (Hearts and Diamonds) contains one card of each rank, including the 10.
- Thus, there is one 10 of Hearts and one 10 of Diamonds.
4. Count the total number of red 10s:
- There are 1 (Ten of Hearts) + 1 (Ten of Diamonds) = 2 red 10s in the entire deck.
5. Calculate the probability:
- Probability is given by the ratio of the number of desired outcomes to the total number of possible outcomes.
- The total number of possible outcomes (total cards in the deck) is 52.
- The number of desired outcomes (red 10s) is 2.
- Therefore, the probability is:
[tex]\[
\text{Probability} = \frac{\text{Number of desired outcomes}}{\text{Total number of possible outcomes}} = \frac{2}{52} = \frac{1}{26}
\][/tex]
So, the probability of drawing a red 10 from a well-shuffled deck of 52 cards is [tex]\(\frac{1}{26}\)[/tex].
The correct answer is:
C. [tex]\(\frac{1}{26}\)[/tex]
