Question

Among 110 students in a probability class, on a three-question exam, 30 get question
1 incorrect, 40 get question 2 incorrect, and 23 get question 3 incorrect. Further, 20
students get both questions 1 and 2 incorrect, 15 get both questions 2 and 3 incorrect,
and 8 get both questions 1 and 3 incorrect, and 7 get all three questions incorrect.

(a) Given that a student gets problem 1 incorrect, what is the probability he gets Prob-
lem 2 incorrect?
(b) Given that a student gets problem 1 correct, what is the probability he gets Problem
2 incorrect?

Answer 1

(c) Given that a student gets both problem 1 and 2 incorrect, what is the probability
he gets Problem 3 incorrect?
(d) Using the definition for the independence of two events, are the events “student gets
problem 1 incorrect” and “student gets problem 2 incorrect” independent? (Show
your work, don’t just answer yes or no.)