B) What is the probability of a person with red hair leaving the room, followed by a persor with blonde hair?

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To determine the probability of a person with red hair leaving the room first, followed by a person with blonde hair, we'll need to make some general assumptions. Let's break it down step by step:

### **Assumptions:**
1. **Total Number of People in the Room (N):** Let's denote the total number of people in the room as $$ N $$.
2. **Number of Red-Haired People (R):** There are $$ R $$ people with red hair.
3. **Number of Blonde-Haired People (B):** There are $$ B $$ people with blonde hair.
4. **No Replacement:** Once a person leaves the room, they don't re-enter (i.e., we're dealing with without replacement).

### **Step-by-Step Calculation:**

1. **Probability that the First Person Leaving is Red-Haired ($$ P_{\text{Red first}} $$):**
   $$
   P_{\text{Red first}} = \frac{R}{N}
   $$
   - **Explanation:** Out of the total $$ N $$ people, $$ R $$ have red hair. So, the probability that the first person leaving is red-haired is the ratio of red-haired individuals to the total number of people.

2. **Probability that the Second Person Leaving is Blonde-Haired Given the First was Red-Haired ($$ P_{\text{Blonde second | Red first}} $$):**
   $$
   P_{\text{Blonde second | Red first}} = \frac{B}{N - 1}
   $$
   - **Explanation:** After one red-haired person has left, there are $$ N - 1 $$ people remaining in the room. Among these, $$ B $$ are blonde-haired. Therefore, the probability that the second person is blonde-haired is the ratio of blonde-haired individuals to the remaining number of people.

3. **Combined Probability:**
   $$
   P_{\text{Red first and Blonde second}} = P_{\text{Red first}} \times P_{\text{Blonde second | Red first}} = \frac{R}{N} \times \frac{B}{N - 1}
   $$
   - **Explanation:** Since both events need to occur in sequence (first red-haired, then blonde-haired), we multiply the probabilities of each independent event.

### **Final Formula:**
$$
\boxed{P = \frac{R}{N} \times \frac{B}{N - 1}}
$$

### **Example:**
Suppose there are **10 people** in the room:
- **3** have red hair ($$ R = 3 $$)
- **4** have blonde hair ($$ B = 4 $$)

The probability would be:
$$
P = \frac{3}{10} \times \frac{4}{9} = \frac{12}{90} = \frac{2}{15} \approx 0.1333 \text{ or } 13.33\%
$$

### **Notes:**
- **With Replacement:** If, for some reason, the first person could re-enter the room before the second leaves (i.e., with replacement), the calculation would differ:
  $$
  P_{\text{With Replacement}} = \frac{R}{N} \times \frac{B}{N}
  $$
- **Order Matters:** The probability calculated is specific to the order—first red-haired, then blonde-haired. If the order were reversed, the probability would be different unless $$ R = B $$.

Feel free to provide specific numbers if you need a numerical answer tailored to a particular scenario!
The probability of a person with red hair leaving the room first, followed by a person with blonde hair is $$ \frac{R}{N} \times \frac{B}{N - 1} $$, where $$ R $$ is the number of red-haired people, $$ B $$ is the number of blonde-haired people, and $$ N $$ is the total number of people in the room.

B) What is the probability of a person with red hair leaving the room, followed by a persor with blonde hair?

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