One card is draw from a pack of 52 cards being equally likely to be drawn . Find the probability of
the card drawn to be red and a king

Answer

To find the probability of drawing a card that is both red and a king from a standard deck of 52 cards, we can follow these steps:

### Step 1: Identify the total number of cards in the deck.
A standard deck of cards has a total of 52 cards.

### Step 2: Identify the total number of red cards in the deck.
In a standard deck, there are two colors: red and black. The red cards consist of hearts and diamonds. Each suit has 13 cards, so:
- Total red cards = 13 (hearts) + 13 (diamonds) = 26 red cards.

### Step 3: Identify the number of kings in the deck.
There are 4 kings in a standard deck, one for each suit (hearts, diamonds, clubs, and spades).

### Step 4: Identify the number of red kings.
Since we are looking for red kings, we only consider the kings from the red suits:
- There are 2 red kings (King of Hearts and King of Diamonds).

### Step 5: Calculate the probability.
The probability of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the favorable outcomes are the red kings, which is 2, and the total outcomes are the total cards in the deck, which is 52.

So, the probability \( P \) of drawing a red king is:
\[ P(\text{Red King}) = \frac{2}{52} = \frac{1}{26} \]

### Final Answer:
The probability of drawing a card that is red and a king is \( \frac{1}{26} \).

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