### 1. Break Down the Problem
- Identify the individual probabilities:
- Probability that P will live 20 years, $ P(P) = \frac{1}{2} $
- Probability that B will live 20 years, $ P(B) = \frac{1}{2} $

### 2. Relevant Concepts
- The events (P living for 20 years and B living for 20 years) are independent. Therefore, the joint probability of both P and B living for 20 years is given by:
$$
P(P \text{ and } B) = P(P) \times P(B)
$$

### 3. Analysis and Detail
- Using the individual probabilities:
$$
P(P \text{ and } B) = \left( \frac{1}{2} \right) \times \left( \frac{1}{2} \right)
$$

### 4. Verify and Summarize
- Performing the multiplication:
$$
P(P \text{ and } B) = \frac{1}{4}
$$

### Final Answer
The probability that both P and B will live for 20 years is $ \frac{1}{4} $.

Question

### 1. Break Down the Problem
- Identify the individual probabilities:
  - Probability that P will live 20 years, $ P(P) = \frac{1}{2} $
  - Probability that B will live 20 years, $ P(B) = \frac{1}{2} $

### 2. Relevant Concepts
- The events (P living for 20 years and B living for 20 years) are independent. Therefore, the joint probability of both P and B living for 20 years is given by:
  $$
  P(P \text{ and } B) = P(P) \times P(B)
  $$

### 3. Analysis and Detail
- Using the individual probabilities:
  $$
  P(P \text{ and } B) = \left( \frac{1}{2} \right) \times \left( \frac{1}{2} \right)
  $$

### 4. Verify and Summarize
- Performing the multiplication:
  $$
  P(P \text{ and } B) = \frac{1}{4}
  $$

### Final Answer
The probability that both P and B will live for 20 years is $ \frac{1}{4} $.

Knowee AI · Accepted Answer

### 1. Break Down the Problem
- Identify the individual probabilities:
  - Probability that P will live 20 years, $ P(P) = \frac{1}{2} $
  - Probability that B will live 20 years, $ P(B) = \frac{1}{2} $

### 2. Relevant Concepts
- The events (P living for 20 years and B living for 20 years) are independent. Therefore, the joint probability of both P and B living for 20 years is given by:
  $$
  P(P \text{ and } B) = P(P) \times P(B)
  $$

### 3. Analysis and Detail
- Using the individual probabilities:
  $$
  P(P \text{ and } B) = \left( \frac{1}{2} \right) \times \left( \frac{1}{2} \right)
  $$

### 4. Verify and Summarize
- Performing the multiplication:
  $$
  P(P \text{ and } B) = \frac{1}{4}
  $$

### Final Answer
The probability that both P and B will live for 20 years is $ \frac{1}{4} $.

If the probability that P will live 20 years is 1/2 and that B will live 20 years is 1/2, then what is the probability that both will live 20 years?

Question

If the probability that P will live 20 years is $\frac{1}{2}$ and that B will live 20 years is $\frac{1}{2}$ , then what is the probability that both will live 20 years?

Solution