Problem:
Johann has fair coins. He flips all the coins. Any coin that lands on tails is tossed again. Coins that land on tails on the second toss are tossed a third time. What is the expected number of coins that are now heads?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
A coin can be tossed once, twice, or three times. View the problem as tossing each coin three times. If all three tosses are tails then the coin ends on a tail; however, if any of the three tosses is a head then the coin ends on a head (the subsequent tosses can be ignored). Thus each coin has a out of chance of landing on heads. Therefore the expected number of heads is .
The problems on this page are the property of the MAA's American Mathematics Competitions