Statistics 1

In-Class Exercise 5

Yu-You Liou

Shih Chien University

2026-09-16

Question 1

Sample Space of Two Dice

Two fair dice are rolled.

1. Build the sample space with expand.grid() and confirm that it contains 36 outcomes with nrow().
2. Find the probability that the sum of the two dice is 7.
3. Find the probability that the sum is at least 10.

Question 2

Classical Probability

A box contains 6 red marbles, 4 blue marbles, and 5 green marbles. One marble is drawn at random.

Compute in R:

1. P(\text{red})
2. P(\text{not red})
3. P(\text{red or blue})

State which rule you used in part 3 and why.

Question 3

Addition Rule with Overlap

Among 200 students, 120 take Statistics, 85 take Accounting, and 45 take both courses.

1. Find the probability that a randomly selected student takes Statistics or Accounting.
2. Find the probability that the student takes neither course.
3. Are the two events mutually exclusive? Explain in one sentence.