A card is drawn from a well shuffled pack of 52 playing cards. The event E is that the card drawn is not a face card. The number of outcomes favourable to the event E is

Options

A. 51
B. 40
C. 36
D. 12

Answer

To solve the problem, we need to determine the number of outcomes favorable to the event E, which states that the card drawn is not a face card. Here’s a step-by-step solution:

### Step 1: Understand the total number of cards
A standard deck of playing cards contains 52 cards.

### Step 2: Identify the face cards
Face cards in a deck consist of Kings, Queens, and Jacks. Each suit (hearts, diamonds, clubs, and spades) has one of each of these face cards:
- Kings: 4 (one from each suit)
- Queens: 4 (one from each suit)
- Jacks: 4 (one from each suit)

### Step 3: Calculate the total number of face cards
To find the total number of face cards, we add the number of Kings, Queens, and Jacks:
\[ \text{Total face cards} = 4 \text{ (Kings)} + 4 \text{ (Queens)} + 4 \text{ (Jacks)} = 12 \text{ face cards} \]

### Step 4: Calculate the number of non-face cards
To find the number of cards that are not face cards, we subtract the number of face cards from the total number of cards:
\[ \text{Non-face cards} = \text{Total cards} - \text{Total face cards} = 52 - 12 = 40 \]

### Step 5: Conclusion
The number of outcomes favorable to the event E (the card drawn is not a face card) is 40.

### Final Answer
The number of outcomes favorable to the event E is **40**.

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