Corrupted by their power, the judges running the popular game show America's Next

Top Mathematician have been taking bribes from many of the contestants. Each episode,

a given contestant is either allowed to stay on the show or is kicked off.

If the contestant has been bribing the judges she will be allowed to stay with probability 1.

If the contestant has not been bribing the judges, she will be allowed to stay with probability

1/3.

Suppose that 1/4 of the contestants have been bribing the judges. The same contestants

bribe the judges in both rounds, i.e., if a contestant bribes them in the first round, she

bribes them in the second round too (and vice versa).

(a) If you pick a random contestant who was allowed to stay during the first episode, what

is the probability that she was bribing the judges?

(b) If you pick a random contestant, what is the probability that she is allowed to stay

during both of the first two episodes?

 

Champlain Bank has a reserve ratio of 5%, $4 million issued in deposits, and $200,000 in actual reserves time your rounded to a whole number a. The bank's initial desired reserves are $ and its initial excess reserves are $ b. If $15,000 in currency is deposited in the bank, its excess reserves become $ c. The money multiplier in this banking system is d. The final amount the money supply can change due to the process of money expansion in the banking system caused by Champlain Bank lending out its excess reserves is $