A conference began at noon with two parallel sessions: 33% of the delegates attended the noon session on portfolio management and 43% of the delegates attended the noon session on chartism. The evening session consisted of a talk by Bill Gates. This was attended by 77% of all delegates. Answer the following questions, rounding your answers to two decimal places where appropriate.

{a} If attendance atthe noon sessions on portfolio management and chartlsm are mutually excluslve. what is 'the probablllty that a randomly chosen delegate attended at least one of these sessions? (b) It attendance at the noon sesslon on portfolio management and the evenlng session are statlstically independent. what Is the probability that a randomly chosen delegate attended at least one of these sessions? {c} Of those attending the noon chartlsm session, 82% also attended the evening sesslon. What is the probabillty that a randome chosen delegate attended at least one of these two sessions