You are playing a game of chance that works this way: First a coin is
drawn at random from a bowl which contains 20 coins.  Then, without anyone
examining the coin, the coin is flipped, placed on a table, and covered.
You are supposed to bet on whether the BOTTOM of the coin is heads or
tails.  9 of the coins have heads on both sides, 10 are ordinary (one head
and one tail) and 11 coins have tails on both sides.

1.  How should you bet?  What are your odds of winning?

2.  Suppose you get to see the top of the coin before you bet on whether
the bottom is heads or tails.  How should you bet?  What are your odds of
winning?
the bottom is heads or tails.  How should you bet?  What are your odds of
winning?


There will be a $1 prize for the best correct solution submitted by a
midshipman.

A solution is "correct" if it answers the question correctly and explains
the answer; a solution is "best" if it includes the clearest correct
explanation.  Solutions are due by noon on Thursday, February 18, 1999.
Submit solutions to Prof. Hanna at mathprob@nadn.navy.mil, or via the
mailbox in Chauvenet 301.

-----------------------------
Two midshipmen submitted correct answers to problem #86, dividing a pile
of coins into two groups, each with the same number of heads showing.  If
there are 199 heads-up coins in the original collection, the simplest
solution is to take any 199 coins from the original group and turn them
all over to form a second group.  Midn. 2/c Friedman and Guzman both got
this solution; Mr. Friedman wins the dollar for the earlier response.


Typo: 30 coins