3.46 A conference began at noon with two parallel sessions.

The session on portfolio management 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 portfolio management session and attendance at the chartism session are mutually exclusive, what is the probability that a randomly chosen delegate attended at least one of these sessions?

b. If attendance at the portfolio management session and attendance at the evening session are statistically independent, 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?