Suppose that it requires at least 10 out of 12 votes from a jury to convict a defendant (i.e., if there are at least 10 guilty votes, the defendant is found guilty; but if there are 9 or less guilty votes, they are found innocent). In addition, suppose that a juror votes innocent for a guilty defendant with a probability 0.2, and they vote guilty for an innocent defendant with probability 0.15. Assuming each juror votes independently, and that 75% of defendants are actually guilty, find the probability that the jury renders the correct decision. (Hint: Letbethe event the jury is correct, and consider two cases). Give your answer to 4 decimal places