A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tickets. The probability that an idividual tourist will not show up is 0.02, independent of all other tourists.

Each ticket costs 50, and is non-refundable if a tourist fails to show up. If a tourist shows up and a seat is not available, the tour operator has to pay 100 (ticket cost + 50 penalty) to the tourist.

What is the expected revenue of the tour operator?

The answer is 984.6. Which makes me wonder why the tour operator wouldn't just sell 20 tickets exactly because then his expected revenue would be 1000. Sometimes the absurdity of the problems distract me from the math. Although I suppose the tour operator might be wondering if it is a good idea to sell that 21st ticket in the first place and then I would tell hir not to. In this case if the penalty was less than 26.4 ze should sell 21 tickets, since it's more than that ze should only sell 20.

...

So I raced Ridge to River on saturday and now I can't walk downstairs very well. I won the women's iron (17th overall) and Koos won the men's iron (3rd overall). I wonder if Koos went tele skiing today like he was talking about... somehow I doubt it -- the 4mi downhill run on pavement then road bike then a good hour in the kayak does NOT make the legs feel good the next day. nope, nope, nope.