Each inhabitant of a remote village always tells the truth or always lies. A villager will only give
a `Yes\' or `No\' answer to a question a tourist asks. Suppose you are a tourist visiting this area
and come to a fork in the road. One branch leads to the ruins you want to visit; the other branch
leads deep into the jungle. A villager is standing at the fork in the road.
(a) What one question can you ask the villager to determine which branch to take? Justify your
answer.
(b) Is it possible to ask a single question and determine both which branch to take and whether
the villager always tells the truth? Justify your answer.
Solution
(a) Point down one road. Ask the villager, \"If someone else were to ask you if this
were the road to the ruins, what would you say?\" If it is the road to the ruins, a truthful villager
would tell someone else the truth, and they\'d tell you the truth about telling the truth, and say
\"yes\". On the other hand, if it is the road to the ruins, a lying villager would lie to someone else,
and they\'d lie to you about lying, and say \"yes\". If isn\'t the road to the ruins, a truthful villager
would tell someone else the truth, and they\'d tell you the truth about telling the truth, and say
\"no\". On the other hand, if isn\'t the road to the ruins, a lying villager would lie to someone
else, and they\'d lie to you about lying, and say \"no\". (b) The particular question in my answer
to (a) tells you which branch to take, but does not distinguish between the two kinds of villagers.
I\'m not sure I can prove there isn\'t a different question that both tells you which branch to take
and distinguishes between the two kinds of villagers. However, if you only get one answer (one
\"yes\" or \"no\"), I don\'t think you can get two pieces of information from it (both the branch
and the type of villager). So I don\'t think it\'s possible, but I\'m not confident my reasoning rises
to the level of a rigorous proof..
Each letter of the word Mississippi is placed on a piece of paper an.pdf
1. Each letter of the word Mississippi is placed on a piece of paper and all 11 pieces of paper are
placed in a hat. The letters are selected at random from the hat and are replaced. Find the
probability that three consonants are selected. Express yourself as a decimal rounded to the
nearest thousandth.
Solution
So thee are 4 vowels and 7 consonants.
The probability of getting three consonants would be as follows:
first consonant * second consonant * third consonant
(7/11) * (6/10) * (5/9) = .212
