The students in a class decide to send a representative to the president of school to complain about their terrible classroom. But nobody in the class will agree to be the representative, so they decide on the following strategy: Each student will toss his/her coin simultaneously; if all the coins but one show the same face, the person who tossed the odd coin must be the representative. If any other combination of heads and tails occurs, the class will toss coins again.

(a) Assuming that there are n students in the class and that all of the coins are fair, what is the expected number of rounds (number of coin tosses each student has to make)? (Hint: Explain why the probability of an odd toss in any given round is p = n/2 n1 . Then explain why the probability of ending on the kth round is (1 p) k1p. Finally, using the method of Example 25 on page 167 of Rosen, get the answer 2n1/n.)

(b) One of the n students decides to cheat and uses a false coin that comes up heads much more often than tails. How does this change the answer in part (a)? Explain