In the United States, criminal defendants are presumed innocent until they are proven guilty beyond a reasonable doubt, because it is thought better to let nine guilty people go free than to send one innocent person to prison. Assume that 90 percent of all defendants are guilty, 90 percent of the guilty defendants are convicted, and 90 percent of the innocent defendants are set free.

a. Of those people convicted, what percent are innocent?

b. Of those people set free, what percent are guilty?