Red queens and black jacks are removed from a pack of `52` playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is a face card

Options

A. `1/2`
B. `3/4`
C. `4/5`
D. `1/6`

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the total number of cards
A standard pack of playing cards contains 52 cards. However, we are removing 2 red queens and 2 black jacks from the pack.

**Total cards removed:**
- 2 Red Queens
- 2 Black Jacks
**Total removed = 2 + 2 = 4 cards**

**Remaining cards = Total cards - Removed cards**
= 52 - 4 = 48 cards

**Hint:** Remember to subtract the number of removed cards from the total number of cards.

### Step 2: Identify the face cards in the remaining cards
Face cards in a standard deck include Kings, Queens, and Jacks.

**Total face cards in a standard deck:**
- Kings: 4
- Queens: 4
- Jacks: 4
**Total face cards = 4 + 4 + 4 = 12**

Now, we need to determine how many face cards are left after removing the specified cards.

**Removed face cards:**
- 2 Red Queens (removed)
- 2 Black Jacks (removed)

**Remaining face cards:**
- Kings: 4 (none removed)
- Queens: 2 (4 - 2 = 2 remaining)
- Jacks: 2 (4 - 2 = 2 remaining)

**Total remaining face cards = Kings + Queens + Jacks**
= 4 + 2 + 2 = 8 face cards

**Hint:** Count the remaining face cards carefully after removing the specified cards.

### Step 3: Calculate the probability of drawing a face card
Probability is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

**Favorable outcomes (face cards) = 8**
**Total outcomes (remaining cards) = 48**

Thus, the probability of drawing a face card is:
\[ P(\text{Face Card}) = \frac{8}{48} \]

### Step 4: Simplify the probability
Now, simplify the fraction:
\[ P(\text{Face Card}) = \frac{8 \div 8}{48 \div 8} = \frac{1}{6} \]

### Final Answer
The probability that the drawn card is a face card is \( \frac{1}{6} \).

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