One cards is drawn from a pack of 52 cards , each of the 52 cards being equally like to be drawn . Find the probability that the card drawn is
either red or king

Answer

To solve the problem of finding the probability that a card drawn from a pack of 52 cards is either red or a king, we can follow these steps:

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

### Step 2: Count the number of red cards
In a standard deck, there are two red suits: hearts and diamonds. Each suit has 13 cards.
- Number of red cards = 13 (hearts) + 13 (diamonds) = 26 red cards.

### Step 3: Count the number of kings
There are 4 kings in a deck (one from each suit: hearts, diamonds, clubs, and spades).
- Number of kings = 4.

### Step 4: Count the number of red kings
Among the 4 kings, 2 of them are red (king of hearts and king of diamonds).
- Number of red kings = 2.

### Step 5: Calculate the number of favorable outcomes
To find the number of favorable outcomes for the event "either red or king," we need to add the number of red cards and the number of kings, but we must subtract the red kings since they have been counted twice.
- Number of favorable outcomes = Number of red cards + Number of kings - Number of red kings
- Number of favorable outcomes = 26 (red cards) + 4 (kings) - 2 (red kings) = 28.

### Step 6: Calculate the probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Total number of outcomes = 52 (total cards).
- Therefore, the probability that the drawn card is either red or king is:
\[ \text{Probability} = \frac{28}{52} \]

### Step 7: Simplify the probability
To simplify \( \frac{28}{52} \):
- Both 28 and 52 can be divided by 4.
- \( \frac{28 \div 4}{52 \div 4} = \frac{7}{13} \).

### Final Answer
The probability that the card drawn is either red or a king is \( \frac{7}{13} \).

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