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)