The full fare is $100, the discounted fare is $70. in the next period (the last one before departure) there will be a request for the discounted fare with probability 0.5, and a full fare request with probability 0.4; probability of no request is 0.1.

$78

Step-by-step explanation:

The two events,i.e request for full fare and the request for discounted fare ar mutually exclusive ,i.e if one happens the other cannot and vice versa .

The representation via set diagram will show a disjointed subset while P(AnB)^° is 1- (P(A)+P(B))=0.1.

Where A is the probability of full fare request while B is the probability of discounted request.

Probability (AUB)=P(A)+ P(B)=0.5×100+0.4×70=78.