Suppose that there is a 2.2% chance a planet will develop life, a 3.1% chance that the life will evolve into complex organisms, a 6.1% chance that complex organisms develop into advanced civilizations, and an X% chance that the advanced civilizations become intergalactic. If there are 1,351,006 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!
Suppose that there is a 2.2% chance a planet will develop life, a 3.1% chance that the life will evolve into complex organisms, a 6.1% chance that complex organisms develop into advanced civilizations, and an X% chance that the advanced civilizations become intergalactic. If there are 1,351,006 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!
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:**Estimating the Probability of Advanced Civilizations Becoming Intergalactic**
*Suppose that there is a 2.2% chance a planet will develop life, a 3.1% chance that the life will evolve into complex organisms, a 6.1% chance that complex organisms develop into advanced civilizations, and an X% chance that the advanced civilizations become intergalactic.*
**Given Data:**
- Total number of planets: 1,351,006
- Observed intergalactic civilizations: 1
**Task:** Determine the expected value of X, the chance that advanced civilizations become intergalactic.
**Note:**
- X is in percentage form (e.g. 30.51 not 0.3051).
- Round to two decimal places, but do not round until the final answer.
---
To find the expected value of X, follow sequential probabilistic steps based on the given percentages and final observations.
Use these guiding probabilities and observed values to solve for X%, ensuring that you maintain precision until the final rounding step.
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