Kate is working on the Extra Practice Problem set in preparation for the exam. Suppose that Kate answers a problem correctly with probability 1/2, independently of all other problems.

(a) (2 points) What is the probability that Kate answers exactly two of the next five problems incorrectly?

(b) (3 points) Kate will continue attempting problems until she answers exactly three questions correctly and then she will watch the news. What is the probability that Kate will need to attempt five questions in total before she is able to watch the news.