Probability Theory
70% of students passed the Mathematics examination, and
60% of students passes the Science examination.
What is the minimum percentage of students that passed both examinations?
In a class of students, \(64\text{%}\) of the students passed the physics exam and \(68\text{%}\) of the students passed the math exam.
What is the minimum percentage of students in the class that passed both exams?
How many numbers in the set \(\{1,2,\ldots,100\}\) are divisible by \(5\) or \(7?\)
A party of \(370\) vile creatures is marching through the woods. Each of the creatures is either an orc, a goblin, or a half-orc/half-goblin. If there are \(206\) creatures that are at least partly goblin, and \(211\) creatures that are at least partly orcs, how many of the creatures are half-orc/half-goblins?
Consider all \(4\)-digit positive numbers using all of the digits \(\{1, 2, 3, 4\}\). How many of these numbers have even first or second digit?