Suppose that there is a 0.9% chance a planet will develop life, a 2.3% chance that the life will evolve into complex organisms, a 7% chance that complex organisms develop into advanced civilizations, and an X% chance that the advanced civilizations become intergalactic. If there are 2,131,984 planets, and we observe only 1 intergalactic civilization, what is the expected value of X? Note that X is in percentage form (e.g. 30.51 not 0.3051). You can round to two decimal places, but do not round until your final answer!

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
icon
Related questions
Question
### Problem Statement:

#### Astrobiology and Probability

---

Suppose that there is a 0.9% chance a planet will develop life, a 2.3% chance that the life will evolve into complex organisms, a 7% chance that complex organisms develop into advanced civilizations, and an X% chance that the advanced civilizations become intergalactic.

If there are 2,131,984 planets, and we observe only 1 intergalactic civilization, what is the expected value of X?

---

**Note:**
- X is in percentage form (e.g., 30.51 not 0.3051).
- You can round to two decimal places, but do not round until your final answer!

---

### Explanation:

Consider each step as a sequential probability process:

1. **Probability that a planet develops life:**  
   \( P(\text{Life}) = 0.009 \)
  
2. **Probability that life evolves into complex organisms, given that life has already developed:**  
   \( P(\text{Complex Organisms}|\text{Life}) = 0.023 \)
  
3. **Probability that complex organisms develop into advanced civilizations, given that complex organisms have developed:**  
   \( P(\text{Advanced Civilizations}|\text{Complex Organisms}) = 0.07 \)
  
4. **Probability that advanced civilizations become intergalactic, given that advanced civilizations exist (this is X, which we need to find):**  
   \( P(\text{Intergalactic}|\text{Advanced Civilizations}) = \frac{X}{100} \) 

### Formulating the Combined Probability:
  
The combined probability for one planet to reach the intergalactic civilization stage is:
\[ 
P(\text{Intergalactic}) = P(\text{Life}) \times P(\text{Complex Organisms}|\text{Life}) \times P(\text{Advanced Civilizations}|\text{Complex Organisms}) \times P(\text{Intergalactic}|\text{Advanced Civilizations}) 
\]

### Setting Up the Equation:
  
With 2,131,984 planets and 1 observed intergalactic civilization:
  \[ 
  1 = 2,131,984 \times 0.009 \times 0.023 \times 0.07 \times \frac{X}{100} 
  \]

\[ 
  1 =
Transcribed Image Text:### Problem Statement: #### Astrobiology and Probability --- Suppose that there is a 0.9% chance a planet will develop life, a 2.3% chance that the life will evolve into complex organisms, a 7% chance that complex organisms develop into advanced civilizations, and an X% chance that the advanced civilizations become intergalactic. If there are 2,131,984 planets, and we observe only 1 intergalactic civilization, what is the expected value of X? --- **Note:** - X is in percentage form (e.g., 30.51 not 0.3051). - You can round to two decimal places, but do not round until your final answer! --- ### Explanation: Consider each step as a sequential probability process: 1. **Probability that a planet develops life:** \( P(\text{Life}) = 0.009 \) 2. **Probability that life evolves into complex organisms, given that life has already developed:** \( P(\text{Complex Organisms}|\text{Life}) = 0.023 \) 3. **Probability that complex organisms develop into advanced civilizations, given that complex organisms have developed:** \( P(\text{Advanced Civilizations}|\text{Complex Organisms}) = 0.07 \) 4. **Probability that advanced civilizations become intergalactic, given that advanced civilizations exist (this is X, which we need to find):** \( P(\text{Intergalactic}|\text{Advanced Civilizations}) = \frac{X}{100} \) ### Formulating the Combined Probability: The combined probability for one planet to reach the intergalactic civilization stage is: \[ P(\text{Intergalactic}) = P(\text{Life}) \times P(\text{Complex Organisms}|\text{Life}) \times P(\text{Advanced Civilizations}|\text{Complex Organisms}) \times P(\text{Intergalactic}|\text{Advanced Civilizations}) \] ### Setting Up the Equation: With 2,131,984 planets and 1 observed intergalactic civilization: \[ 1 = 2,131,984 \times 0.009 \times 0.023 \times 0.07 \times \frac{X}{100} \] \[ 1 =
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON