A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a heart or a king.

Options

A. `4/13`
B. `9/13`
C. `8/13`
D. `11/26`

Answer

To find the probability of drawing a heart or a king from a well-shuffled deck of 52 cards, we can follow these steps:

### Step 1: Identify the Total Number of Cards
In a standard deck of cards, there are a total of 52 cards.

**Hint:** Remember that a standard deck consists of 4 suits: hearts, diamonds, clubs, and spades.

### Step 2: Count the Number of Hearts
In the deck, there are 13 hearts.

**Hint:** Each suit (hearts, diamonds, clubs, spades) contains 13 cards.

### Step 3: Count the Number of Kings
There are 4 kings in total in the deck (one from each suit).

**Hint:** Each suit has one king, so count the kings from all four suits.

### Step 4: Identify the Overlap
Since one of the kings is also a heart (the King of Hearts), we need to ensure we do not double-count it.

**Hint:** When calculating probabilities for "or" events, subtract any overlap to avoid counting it twice.

### Step 5: Calculate the Total Favorable Outcomes
The total number of favorable outcomes for drawing a heart or a king can be calculated as follows:
- Total hearts = 13
- Total kings = 4
- Overlap (King of Hearts) = 1

So, the total favorable outcomes = Number of hearts + Number of kings - Overlap
= 13 + 4 - 1 = 16

**Hint:** Use the formula: P(A or B) = P(A) + P(B) - P(A and B).

### Step 6: Calculate the Probability
The probability of drawing a heart or a king is given by the formula:
\[ P(\text{Heart or King}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:
\[ P(\text{Heart or King}) = \frac{16}{52} \]

### Step 7: Simplify the Probability
Now, simplify the fraction:
\[ P(\text{Heart or King}) = \frac{16 \div 4}{52 \div 4} = \frac{4}{13} \]

### Final Answer
The probability of drawing a heart or a king from a deck of 52 cards is \( \frac{4}{13} \).

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