Jury selection

Consider a jury trial whose underlying issue is so polarizing that the trial's outcome is predetermined by jury selection: the arguments of the trial are irrelevant. Suppose that proportion p of the population believe guilt and (1-p) believe innocence, from which a jury pool of 12+2n will be selected. Both the prosecution and defense each remove n candidates during voir dire, leaving 12. (Is this how jury selection really works?) Assume, for now, that both parties can accurately predict a juror's vote. What is the probability that the jury will be unanimous for one side or the other?

If a jury hangs, due to non-unanimity, a mistrial is declared. Assume the prosecution will keep re-prosecuting the case until a verdict is returned. As a function of p, what are the probabilities of the eventual verdict (in which, by chance, greater than 12+n of the original pool favored one side)? How many trials does it take?

This model may be made more complicated by allowing errors in each party's ability to "read" a juror, possibly asymmetric. Game theoretically, jurors may choose to lie about how they feel in order to avoid being excused.