Jurors are not supposed to discuss a case with anyone until after all of the evidence has been presented. They then retire to the jury room for deliberations, which sometimes begin with a secret-ballot vote of the jurors. Suppose that we have a case where each selection of a person for the jury has a 0.9 probability of picking someone who, after hearing all of the evidence, would initially vote guilty and a 0.1 probability of picking someone who would initially vote not guilty. What is the probability that the initial vote will be unanimously guilty if there is a

a. 12-person jury?

b. 6-person jury?