A card is drawn at randown from a well shuffled deck of playing cards. Find the probability that the card drawn is
a card of spade or an ace

Answer

To find the probability of drawing a card that is either a spade or an ace from a well-shuffled deck of playing cards, we can follow these steps:

### Step 1: Identify the Total Number of Cards
A standard deck of playing cards contains 52 cards.

**Hint:** Remember that a standard deck has 4 suits: hearts, diamonds, clubs, and spades, each containing 13 cards.

### Step 2: Count the Number of Spades
In a deck, there are 13 spades.

**Hint:** Recall that each suit has the same number of cards.

### Step 3: Count the Number of Aces
There are 4 aces in a deck (one for each suit: hearts, diamonds, clubs, and spades).

**Hint:** Think about how many suits there are and how many aces are in each suit.

### Step 4: Identify the Overlap (Ace of Spades)
The ace of spades is counted in both the spades and the aces. Therefore, we need to account for this overlap.

**Hint:** Consider how many cards fall into both categories (spades and aces).

### Step 5: Use the Probability Formula
To find the probability of drawing a spade or an ace, we use the formula for the union of two events:
\[ P(S \cup A) = P(S) + P(A) - P(S \cap A) \]
Where:
- \(P(S)\) is the probability of drawing a spade.
- \(P(A)\) is the probability of drawing an ace.
- \(P(S \cap A)\) is the probability of drawing the ace of spades.

### Step 6: Calculate Each Probability
- The probability of drawing a spade:
\[ P(S) = \frac{13}{52} \]
- The probability of drawing an ace:
\[ P(A) = \frac{4}{52} \]
- The probability of drawing the ace of spades (the overlap):
\[ P(S \cap A) = \frac{1}{52} \]

### Step 7: Substitute Values into the Formula
Now, substituting the values into the formula:
\[ P(S \cup A) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} \]

### Step 8: Simplify the Expression
Combine the fractions:
\[ P(S \cup A) = \frac{13 + 4 - 1}{52} = \frac{16}{52} \]

### Step 9: Reduce the Fraction
Now, simplify \(\frac{16}{52}\):
\[ P(S \cup A) = \frac{4}{13} \]

### Final Answer
The probability that the card drawn is a spade or an ace is \(\frac{4}{13}\).

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