A conference began at noon with two parallel sessions. The session on portfolio manage- ment was attended by 40% of the delegates, while the session on chartism was attended by 50%. The evening session consisted of a talk titled, "Is the random walk dead?" This was attended by 80% of all delegates.

(a) If attendance at the sessions on portfolio management and chartism are mutually ex- clusive, what is the probability that a randomly chosen delegate attended at least one these sessions? of

(b) If attendance at the portfolio management and evening sessions are statistically inde- pendent, what is the probability that a randomly chosen delegate attended at least one of these sessions?

(c) Of those attending the chartism session, 75% also attended the evening session. What is the probability that a randomly chosen delegate attended at least one of these two sessions?