# Lesson 1

Up to Chance

- Let’s explore chance.

### Problem 1

What is the probability of the spinner landing on the section labeled G?

\(\frac{1}{2}\)

\(\frac{1}{4}\)

\(\frac{1}{5}\)

\(\frac{1}{8}\)

### Problem 2

This spinner is spun 1,000 times. Which of these is the best estimate for the number of times it would be expected to land on the section labeled B?

16

60

160

600

### Problem 3

On an assignment, there are two true or false questions. You have no idea what the correct answer is to either one so you guess.

- What is the probability that you get both of them right by guessing? Explain your answer.
- What is the probability that you get exactly one of them right by guessing? Explain your answer.

### Problem 4

- Find the length of an arc with central angle \(\frac{2\pi}{3}\) radians and a radius of 7 units.
- Find the length of an arc with central angle \(\frac{\pi}{4}\) radians and a circumference of \(10\pi\) units.
- Find the measure (in radians) of a central angle of an arc with arc length 12 units and radius 3 units.

### Problem 5

In the circle, sketch a central angle that measures \(\frac{\pi}{2}\) radians.

### Problem 6

The circle in the image has been divided into congruent sectors. What is the measure of the central angle of the shaded region in radians?

\(\frac{1}{12}\) radians

\(\frac{\pi}{12}\) radians

\(\frac16\) radians

\(\frac{\pi}{6}\) radians

### Problem 7

Select **all** true statements.

The incenter of a triangle is the intersection of the angle bisectors.

The incenter is the same distance from all the vertices of the triangle.

The incenter is the same distance from all sides of the triangle.

In order to construct the incenter, all 3 angle bisectors must be constructed.

The incenter is the intersection of the perpendicular bisectors of each side.