Note that each problem provides a hint which should guide you through the problem along with the
Example Problem as a reference.
Post any questions you have to the General Discussion area.
Problem 1:
You are taking a 10 question multiple choice test. If each question has four choices and you
guess on each question, what is the probability of getting one question correct?
[Hint: This is a binomial
in the form of 10 choose 1 with p=.25.]
■
10!/((10-1)!*1!)*(0.25^1)*(1-0.25)^(10-1)
■
10*0.25*0.75^9
■
0.1877 or 18.77%
Problem 2:
What is the probability of getting seven questions correct?
[Hint: This is a binomial as Q1
with modified choose value.]

Problem 3:
What are your chances of answering seven questions correctly if you can reliably eliminate
one possible answer from each question?
[Hint: This is a binomial as Q2 with a modified p value.]

Problem 4:
Let’s say, instead, that the test is an adaptive test; you get to answer more questions based
on your previous success.
This test is structured like this:
●
First you have to answer three questions and if you are correct on two of them, you get to answer three
more questions.
●
If two of
those
are correct, then you get three final questions, of which you need to get at least two
correct to pass the whole test.
The test details are:
●
The first test, T1, has three multiple choice questions with four possible answers each (
p
=0.25 per
question).
●
The second test, T2, has three multiple choice questions with three possible answers each (
p
=0.33 per
question).

●
The final test, T3, has three questions that are true/false (
p
=0.50 each question).
The test questions are formed as follows:
●
The questions are in a language you have never seen: a mixture of Navaho, Swahili, Klingon, and
Esperanto. So you have to guess on all of the questions and there are no contextual clues to eliminate
any answers. This is the first one:
'Arlogh Qoylu'pu'?
Moja: Yel kholgo eeah.
Mbili: Floroj kreskas ĉirkaŭ mia domo. Pe'el!
Tatu: La sandviĉo estos manĝota'mo'tlhIngan maH!
Nne: 'Adeez'æ`q eeah.
(The professor sits at the front of class with a giant, sadistic grin while the students
throw wads of paper at his head.)
Using the binomial probability rule, the law of total probability and Bayes’ theorem:
a)