We live in an era where conspiracy theories are everywhere. I'm sure you've all heard of, or perhaps even believe in, one of them.
I am skeptical of most of them. A common retort to my skepticism is the following:some conspiracy theories are true!Of course, this is correct. Many clandestine operations have occured in high political and corporate circles. But how do we know? Because someone spilled the beans!
One of the main argumentsagainstseveral conspiracy theories' existence hinges on a simple fact: many people are not good at keeping secrets.This can be problematic when we attempt to understand how many people must be involved in many alleged conspiracies. For example, if the moon landing was faked, there would be many people aware of the truth: photographers, set designers, and politicians among others. It seems probable that if the moon landing was actually faked, we would know by now.
Using mathematics, we can demonstrate this.
Consider the following scenario. Suppose that 1000 people are involved in a conspiracy. Suppose that every single individual involved in the conspiracy can be trusted 99.9%, that is, there is a 0.01% probability they reveal the secrets of the conspiracy to the media within 50 years. This probability is the same for everyone involved, and never changes over the course of the 50 years. Moreover, suppose that the event where anyone goes to the media (or not) is independent if anyone else has (or hasn't) already.
What is the probability thatat least one personinvolved in the conspiracy reveals their involvement to the media within 50 years? Do not just speculate. Demonstrate the reasoning behind your answer. This is a problem that can be solved with the techniques of Chapter 5.