I read the following passage in Barabasi - Bursts (http://www.amazon.com/Bursts-Hidden-Pattern-Behind-Everything/dp/0525951601)
A 12 member jury make a correct verdict 80 percent of the time and an incorrect 20 percent of the time.
P verdict | guilty: .8
P verdict | not guilty: .2
The probability of all juries making an incorrect verdict is therefore $.2^{12} = 0.000000004$.
I also know that the outcome preferred by the majority of jurys, before the jury discussed the case coincided with the final verdict 91 percent of the time.
Now what I don't understand is the following:
Therefore, to calculate the outcome of a verdict it is sufficient to consider the view of the majority. We can adjust our above calculation to do just that, and now the probability that the twelve-member jury will wrongly convict an innocent defendant jumps from 0.000000004 to 0.4 percent
I'm trying to figure out how this calculation was 'adjusted' but I can't.
Can someone help?