Question

Fact Suppose there are n distinct objects. There are (n above k) possible ways to remove k objects. You only need to express your answers in the “n-choose-k” notation. For the following questions, it might be helpful to rst write down the sample space.

1. There are 4 balls. Draw 2 balls. Each pair of balls is equally likely to be drawn. What is the probability that the outcomes are either (1, 2) or (1, 3)?

2. There are 4 balls. Draw 2 balls randomly. Each pair of balls is equally likely to be drawn. What is the probability that the outcomes include ball 3?

3. There are 5 restaurants on a straight street. Health inspectors randomly choose 2 out of the 5 restaurants. Each pair is equally likely to be drawn. What is the probability that the two restaurants are adjacent to each other? 1

4. There are N sports teams. They are randomly assigned into pairs in the current round, i.e., every possible assignment is equally likely. Viewers wish that team A and B do not meet in the current round. What is the probability that these two teams do meet?

5. Suppose that there is a box of four balls marked 1, 10, 100, 1000. Two balls are randomly taken from the box and the numbers added together. Each pair of balls is equally likely to be drawn. What are the possible sums? Which one is the most likely?

6. Suppose that there is a box of four balls marked 1, 1, 0, 0. Two balls are randomly taken from the box. Each pair of balls is equally likely to be drawn. What are the possible sums? Which one is the most likely?

Answer 1