0.75 (or 75%) of students pass the midterm. Among those passing the midterm, 0.86 pass the final exam. Among those that fail the midterm, 0.53 pass the final exam. (A tree diagram or a 1-by-1 square is helpful) a. If a student is randomly selected from the entire group, what is the probability the student passes both midterm and final? Correct (answer an exact decimal between 0 and 1.) Hint: this is an unconditional probability, and it is one of the "atoms" of your tree or square. b. If a student is randomly selected and is then discovered to have passed the final, what is the posterior probability that the student passed the midterm given knowledge of this discovery?