Probability and Counting Exercises 1 Probability and Counting

Probability and Counting Exercises 1

Probability and Counting Exercises Suppose X is a finite set of x elements and Y is a finite set of y elements. How many different functions from X to Y ? How many different relations from X to Y ? 2

Probability and Counting Exercises In the World Cup soccer game finals, there are 32 teams that need to be divided to 8 different groups with 4 teams per group. How many different group results? 1. If the group names (Group A, B, C, …H) matter 2. If the group names do not matter 3

Probability and Counting Exercises What is the probability that a randomly chosen 4 -digit integer has distinct digits and is odd? 4

Probability and Counting Exercises There are 100 students and three courses, CS, MATH, and ENGLISH to take. We know 28 students are taking CS, 26 students are taking MATH, and 14 are taking ENGLISH, 8 students are taking both CS and MATH, 4 students are taking both CS and ENGLISH, and 3 students are taking both MATH and ENGLISH, 2 students are taking all three courses. How many students are taking at least one course? How many students are not taking any course? How many students are taking CS and MATH but not ENGLISH? How many student are taking MATH but neither of the other two? 5

Probability and Counting Exercises There are two exam for a certain course. 25% students in class got 90+ in the first exam, and 15% students in class got 90+ in both exams. What percentage of students who got 90+ in the first exam also got 90+ in the second exam? 6

Probability and Counting Exercises Two different factories both produce a certain automobile part. The defective rate of the first factory is 2%, and the defective rate of the second factory is 5%. In a supply of 180 such automobile parts, 100 were from the first factory and 80 were from the second factory. What the probability that a part chosen at random from the 180 is from the first factory? What the probability that a part chosen at random from the 180 is defective? If a randomly chosen part is defective, what is the probability that it came from the first factory? 7