one day, an elf jumps out at you from behind a garbage can and proposes a wager. he says that if the weather in leipzig, germany tomorrow is sunny, he'll give you $20, if it's cloudy (but dry) he'll give you $1, but if neither of those are the case you owe him $15. helpfully, he also provides you data that indicates that the probability of sunny weather in leipzig tomorrow is 40% and cloudy-but-dry is 10%. how much do you expect to win or lose from this wager (if you accept it)?