Sarah has a lie detector that is 97% accurate. If someone is lying, it will indicate that with probability .97, and if someone is telling the truth, it will also indicate that with probability .97. Sarah decides to test it on 30 of her friends. Knowing that exactly two of them conspired to copy her work, she questions all of them to see who committed this crime. Assume that the results for all of her friends are independent of each other, and that all of them will claim that they are innocent.

a. What is the probability that a friend is lying given that the lie detector says they are lying?

b. What is the probability that the lie detector correctly determines the guilt or innocence of all Sarah's friends?