I'm reading this book (Implementation: How Great Expectations in Washington Are Dashed in Oakland. 1973) and they discuss how hard it is to gain agreement of actors.
They set up a conceptual problem to illustrate this.
Assume that in any chain of decisions, the contracting parties have an 80% probability of reaching an agreement to proceed. Now assume that there are 70 separate agreements that much be reached. What is the probability that all 70 agreements will be successful.
They report that with an 80% probability of agreement, the probability of success after 70 agreements is 0.000000125 and that the number of agreements that reduce the probability to below 50 percent is 4.
The thing is: they do not really explain how they arrive at these probabilities. So, that's why I'm turning to you.
It seems like what is going on here is an exercise in the binomial distribution. Given an 80% probability of a successful trial, what is the probability that 70 trials will return all successes?
To put this in the language of coin tosses: If we assume a coin has a probability of turning up heads of 80%, and we flip the coin 70 times, what is the probability that you would get heads 70 straight times?
Have I got this right?
Thanks for any insight. Thanks, Simon
I hope I've explained myself