To find the probability of drawing an Honor card or a Black card from a standard deck of 52 cards, we can follow these steps:
### Step 1: Identify Honor Cards
Honor cards in a standard deck consist of the Ace, King, Queen, and Jack. There are 4 suits (hearts, diamonds, clubs, and spades), and each suit has one of each of these cards.
- **Total Honor Cards = 4 cards (Ace, King, Queen, Jack) × 4 suits = 16 Honor Cards.**
### Step 2: Identify Black Cards
In a standard deck, there are two black suits: clubs and spades. Each suit has 13 cards.
- **Total Black Cards = 13 cards (clubs) + 13 cards (spades) = 26 Black Cards.**
### Step 3: Identify Overlap (Black Honor Cards)
Some of the Honor cards are also Black cards. The black suits (clubs and spades) contain the following Honor cards:
- Black Honor Cards: Ace, King, Queen, Jack of Clubs, and Ace, King, Queen, Jack of Spades.
- **Total Black Honor Cards = 4 (one for each Honor card in the black suits).**
### Step 4: Calculate Total Favorable Outcomes
To find the total number of favorable outcomes for drawing either an Honor card or a Black card, we need to add the number of Honor cards and Black cards, then subtract the overlap (Black Honor cards) to avoid double counting.
- **Total Favorable Outcomes = Total Honor Cards + Total Black Cards - Total Black Honor Cards**
- **Total Favorable Outcomes = 16 + 26 - 4 = 38.**
### Step 5: Calculate Probability
The probability of an event is given by the formula:
\[
\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}}
\]
In this case, the total outcomes are the total number of cards in the deck, which is 52.
- **Probability = \(\frac{38}{52}\)**
### Step 6: Simplify the Probability
Now we can simplify the fraction:
\[
\frac{38}{52} = \frac{19}{26}
\]
Thus, the probability of drawing an Honor card or a Black card is \(\frac{19}{26}\).
### Final Answer
The probability of choosing an Honor card or a Black card is \(\frac{19}{26}\).
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