Two cards are drawn one by one randomly from a pack of 52 cards. Then find the probability that both of them are king.

Explanation

To find the probability that both cards drawn from a pack of 52 cards are Kings, we can follow these steps:

### Step 1: Determine the total number of cards and the number of favorable outcomes.
- A standard deck has 52 cards.
- There are 4 Kings in a deck (one for each suit: hearts, diamonds, clubs, and spades).

### Step 2: Calculate the probability of drawing the first King.
- The probability of drawing a King on the first draw is given by the number of Kings divided by the total number of cards:
\[ P(\text{First King}) = \frac{4}{52} \]

### Step 3: Calculate the probability of drawing the second King after the first King has been drawn.
- After drawing one King, there are now 51 cards left in the deck, and only 3 Kings remaining.
- The probability of drawing a King on the second draw is:
\[ P(\text{Second King | First King}) = \frac{3}{51} \]

### Step 4: Calculate the combined probability of both events.
- Since the two draws are dependent events (the outcome of the first affects the second), we multiply the probabilities:
\[ P(\text{Both Kings}) = P(\text{First King}) \times P(\text{Second King | First King}) = \frac{4}{52} \times \frac{3}{51} \]

### Step 5: Simplify the expression.
- Now, we can simplify the expression:
\[ P(\text{Both Kings}) = \frac{4 \times 3}{52 \times 51} = \frac{12}{2652} \]
- Simplifying \(\frac{12}{2652}\) gives:
\[ P(\text{Both Kings}) = \frac{1}{221} \]

### Final Answer:
The probability that both cards drawn are Kings is \(\frac{1}{221}\).

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