The jack, queen, king and 8, all of diamonds are lost from a pack of 52 playing cards. If a card is drawn from the remaining well-shuffled pack, then find the probability of getting a
(a) Queen card
(b) Red card
(c) Red king card.

Options

A. `{:((a),(b),"(c)"),(1/12,1/12,1/24):}`
B. `{:((a),(b),"(c)"),(1/16,3/16,1/24):}`
C. `{:((a),(b),"(c)"),(1/16,1/12,1/48):}`
D. `{:((a),(b),"(c)"),(1/16,11/24,1/48):}`

Answer

To solve the problem, we need to calculate the probabilities of drawing specific types of cards from a modified deck of playing cards. Let's break it down step by step.

### Given:
- A standard deck has 52 cards.
- The following cards are lost: Jack, Queen, King, and 8 of Diamonds.
- Remaining cards = 52 - 4 = 48 cards.

### Step 1: Probability of getting a Queen card
1. **Identify the remaining Queens**:
- There are 4 Queens in total: Queen of Diamonds, Queen of Hearts, Queen of Clubs, Queen of Spades.
- Since the Queen of Diamonds is lost, the remaining Queens are: Queen of Hearts, Queen of Clubs, and Queen of Spades.
- Total remaining Queens = 3.

2. **Calculate the probability**:
\[ \text{Probability of getting a Queen} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{3}{48} \]
- Simplifying \(\frac{3}{48}\):
\[ \frac{3}{48} = \frac{1}{16} \]

### Step 2: Probability of getting a Red card
1. **Identify the remaining Red cards**:
- There are 26 Red cards in total (13 Diamonds + 13 Hearts).
- Diamonds: Originally 13, but 4 cards (Jack, Queen, King, 8 of Diamonds) are lost, leaving 9 Diamonds.
- Hearts: All 13 Hearts remain.
- Total remaining Red cards = 9 (Diamonds) + 13 (Hearts) = 22.

2. **Calculate the probability**:
\[ \text{Probability of getting a Red card} = \frac{22}{48} \]
- Simplifying \(\frac{22}{48}\):
\[ \frac{22}{48} = \frac{11}{24} \]

### Step 3: Probability of getting a Red King card
1. **Identify the remaining Red Kings**:
- There are 2 Red Kings in total: King of Diamonds and King of Hearts.
- The King of Diamonds is lost, leaving only the King of Hearts.

2. **Calculate the probability**:
\[ \text{Probability of getting a Red King} = \frac{1}{48} \]

### Final Answers:
- (a) Probability of getting a Queen card = \(\frac{1}{16}\)
- (b) Probability of getting a Red card = \(\frac{11}{24}\)
- (c) Probability of getting a Red King card = \(\frac{1}{48}\)