There is a 375 chance of getting two questions right

3 − 2 )
=
3 !
( 3 − 2 ) ! 2 !
× .5
2
× .5
1
= 3 × .25 × .5 = .375
There is a 37.5% chance of getting two questions right on T3 (the third sub-exam).
b) What are your overall chances of passing the entire exam?
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)
1. (Swahili): From dawn to setting sun. (Navajo)
2. (Swahili): Flowers grow around my house (Esperanto) so all of you may come in.
(Klingon)
3. (Swahili): The sandwich will be eaten (Esperanto) because we are Klingons! (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?