A jury of 12 begins with the premise that the accused is innocent. Assume that these 12 jurors were chosen from a large population, such as voters. Unless the jury votes unanimously for conviction, th...

A jury of 12 begins with the premise that the accused is innocent. Assume that these 12 jurors were chosen from a large population, such as voters. Unless the jury votes unanimously for conviction, the accused is set free.

(a) Evidence in the trial of an innocent suspect is enough to convince half of all jurors in the population that the suspect is guilty. What is the probability that a jury convicts an innocent suspect?

(b)  What type of error (Type I or Type II) is committed by the jury in part (a)?

(c) Evidence in the trial of a guilty suspect is enough to convince 95% of all jurors in the population that the suspect is guilty. What is the probability that a jury fails to convict the guilty suspect?

(d)  What type of error is committed by the jury in part (c)?