Ptotal pt1 x ppassingt1 pt2 x ppassingt2 pt3 x

p(Total) = (p(%T1) x p(Passing|T1)) + (p(%T2) x p(Passing|T2)) + (p(%T3) x
p(Passing|T3))
=(0.333 x .1406) + (0.333 x .2219) + (0.333 x .375)
=.0468 + .0739 + .1249 = .2456 or 24.56%
c) What are your chances of passing T3 if you first pass T1 and T2?
Problem Hint:
 Structure your analysis.
 Figure out the component probabilities: p(passing test 1), p(passing test 2), p(passing
test 3).
 Make a table of their proportional contributions of probability to the whole.
 Calculate the total probability: p(Total).
 Continue using Bayes’ theorem to calculate the probability of passing test 3 conditional
on passing tests 1 and 2.
 Render your interpretation. Use the interpretation in the example as a template, if you
are unsure of what to say.

Problem 5 : Now, let’s say that you know just enough of these obscure languages to translate the first
question in T1:
What time is it? (Klingon)
4. (Swahili): It’s mid-afternoon. (Navajo) [correct answer]
Now the probability of passing T1 has changed because you only have to guess correctly on one of the
two remaining questions in the first section, a one-in-two chance.
a) What is the new probability for T1?
b) Now what is the overall probability of passing the entire test?
c) And what is the probability of passing section T3, given that you have already passed
sections T1 and T2?
d) The kicker: How do you explain the difference between 4c and 5c? Can you relate this to a
larger context about conditional probability and making decisions?

Problem Hint:
 Compute the new probability for T1
 Derived the total probability using the new value of T1
 Use Bayes theorem with the updated values to compute new conditional probability of
passing T3 given you have passed T1 and T2
 Consider conditional probability and how T1, T2 and T3 are considered a systems