A teacher tells three boys, Drew, Chris, and Jason, that two of them will have to stay after school to help her clean erasers and that one of them will be able to leave. She further says that she has made the decision as to who will leave and who will stay at random by rolling a special three-sided Dungeons and Dragons die. Drew wants to leave to play soccer and has a clever idea about how to increase his chances of doing so. He figures that one of Jason and Chris will certainly stay and asks the teacher to tell him the name of one of the two who will stay. Drews idea is that if, for example, Jason is named, then he and Chris are left and they each have a probability .5 of leaving; similarly, if Chris is named, Drews probability of leaving is still .5. Thus, by merely asking the teacher a question, Drew will increase his probability of leaving from 1 3 to 1 2 . What do you think of this scheme?

C 12/ C13 expected value/ risk Expected value: if we repeat an experiment many, many times under the same conditions, and if we average the results, then this average is called the expected value Probability= long-run relative frequency Expected value= long- run average Properties for discrete r.v. (X) o 0 < pi < 1, for each i o Sum of all probabilities is 1 A “fair bet”: one in which the expected value of the winnings is zero Bigger variance more risk