You are given choice of four envelops. Inside one envelop is $240; inside the others, fake bills. You pick one envelop but do not open it. Of the three remaining envelopes, one of the empty envelops is opened and revealed. You are offered the choice to pick one of the other two untouched envelops. However, you are told that if you switch your pick and subsequently end up with envelop with the real bill, you only keep a fraction, p, of the amount in there.
A) What is the value of p that will make you indifferent about switching your initial pick or not?
B) Finally, in a similar scenario but with n number of envelops, what is p? In other words, what is the function p(n)?