DAT 520 Problem Set 3
Cumulative and Conditional Probability
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.]

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.