A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a jack.

Answer

To find the probability that a card drawn from a pack of 52 playing cards is neither an Ace nor a Jack, we can follow these steps:

### Step 1: Identify the total number of cards
In a standard deck of playing cards, there are a total of 52 cards.

### Step 2: Identify the number of Aces and Jacks
In a deck, there are 4 Aces and 4 Jacks.

### Step 3: Calculate the total number of Aces and Jacks
The total number of Aces and Jacks combined is:
\[ 4 \text{ (Aces)} + 4 \text{ (Jacks)} = 8 \]

### Step 4: Calculate the number of favorable outcomes
To find the number of cards that are neither Aces nor Jacks, we subtract the total number of Aces and Jacks from the total number of cards:
\[ 52 \text{ (total cards)} - 8 \text{ (Aces and Jacks)} = 44 \]

### Step 5: Calculate the probability
The probability of drawing a card that is neither an Ace nor a Jack is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we have:
\[ \text{Probability} = \frac{44}{52} \]

### Step 6: Simplify the fraction
To simplify \( \frac{44}{52} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[ \frac{44 \div 4}{52 \div 4} = \frac{11}{13} \]

### Final Answer
Thus, the probability that the card drawn is neither an Ace nor a Jack is:
\[ \frac{11}{13} \]

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