Question

Problem (2) You are in a race around the world, and can choose to travel to a nearby
city by horse, car, or train. Because you tend to travel to a cities with high amounts
of trac, there is a 20% chance that another contestant will arrive before you if you
travel by car. When you travel by horse, you can take di erent routes but the mode of
transportation is very slow so there is a 60% chance that another contestant will arrive
before you. Traveling by train is very reliable and leaves only a 10% chance that another
contestant will arrive before you.
(2A) Suppose another contestant learns that you have arrived at the next destination,
but that someone else has beaten you there. What will they conclude is the probability
that you traveled by car? The probability you traveled by horse? The probability you
traveled by train?

(2B) The contestant must now select which mode of transportation they will take. They
are only allowed to select a mode of transportation you did not take. Assume the contes-
tant always selects the mode of transportation you are least likely to have taken (if there
is a tie, you may assume the contestant randomly picks). What is the probability that
they have selected a mode of transportation they are \allowed" to take?

Answer 1