Suppsoe it takes at least 10 votes of guilty from a 12-member jury to convice a defendant. Suppose that the probability an individual juror votes a guilty person innocent is 0.2, whereas the probability a juror votes an innocent person guilty is 0.1, and assume jurors reach their decisions independently.
(a) What is the distribution of the number of votes of guilty if the defendant is innocent, and if they are guilty?
(b) Find the probability a defendant is convicted given that he is guilty, and find the probability a defendant is convicted given that he is innocent.
(c) If 65% of all defendants are guilty, what is the probability the jury reaches the correct decision on a randomly selected defendant?
(d) Again, if 65% of all defendants are guilty, what is the probability that a convicted defendant is actually innocent?
Does anyone know how to do this? I don't understand part (a) and think i may need that for the other parts?