The organizers of an outdoor 2-day (Friday/Saturday) concert are hoping for sunny weather. They have heard the following information about the weather forecast:

70% chance of sun on at least one of the two days

50% chance of sun Friday

45% chance of sun Saturday

(a) Find each of the following four probabilities (these correspond to the regions of a 2-circle Venn diagram with one circle for "sun on Friday" and the other circle for "sun on Saturday":

P(sun on Friday only)

P(sun on Saturday only)

P(sun both days)

P(no sun either day)

(b)For the Friday concert, the organizers think they will sell 30,000 tickets if the weather is sunny, but only 10,000 tickets otherwise. For the Saturday concert, they think they will sell 50,000 tickets if the weather is sunny, but only 20,000 tickets otherwise.

Based on this information, what is the expected number of tickets they will sell? Compute the numerical value, and show enough work to make your understanding clear.