(1) I am playing Guess Who with my son, the goal of which is to guess which card (which person's face)
your opponent has before they guess which one you have. Players take turns asking questions (whose
answers must be "yes" or "no") about their opponent's card such as "does your person have brown
eyes?" or "is your person wearing glasses?" A player wins if they say "Is your person [NAME]" where
NAME) is the name of the person on the opposing player's card.
Assume it is my turn to ask a question and I have narrowed my son's card down to being one
of four people, while my son has narrowed my card down to being one of three people. If I expect
my son to randomly guess a remaining person on each of his turns, would I be better off asking
a question that would definitely let me narrow my son's person down to two possibilities (eg. "is
the person wearing glasses?" when two of the four remaining are wearing glasses), then randomly
guessing specific people on subsequent turns? ...or should I start randomly guessing people now when
there are four possibilities and keep guessing randomly on every subsequent turn until the game is
over? ...or does it not matter which strategy I use?
[Hint: Break your calculation into cases and calculate the probability my son guesses correctly
on his next turn, vs. on his one after that, vs. the one after that. Remember he has three possibili-
ties to guess so would definitely guess my person on one of his next 3 turns.