# Lesson 2

Playing with Probability

### Problem 1

Six papers are placed in a bag with names written on them. The names are: Lin, Mai, Mai, Noah, Priya, and Priya. If one name is chosen at random, what is the probability that it is Priya?

A:

$$\frac{1}{4}$$

B:

$$\frac{1}{6}$$

C:

$$\frac{2}{4}$$

D:

$$\frac{2}{6}$$

### Problem 2

Select all of the words for which the probability of selecting the letter E at random is $$\frac{1}{3}$$.

A:

THE

B:

BEST

C:

SNEEZE

D:

FREES

E:

SPEECH

### Problem 3

Design a situation where the probability of one event is $$\frac{1}{5}$$ and another event is $$\frac{1}{10}$$. Explain your reasoning.

### Problem 4

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

A:

$$\frac{1}{8}$$

B:

$$\frac{1}{5}$$

C:

$$\frac{1}{4}$$

D:

$$\frac{1}{2}$$

### Solution

(From Unit 8, Lesson 1.)

### Problem 5

This spinner is spun 300 times. Estimate the number of times it would be expected to land on the section labeled B.

### Solution

(From Unit 8, Lesson 1.)

### Problem 6

A circle has radius 5 units. For each angle measure, find the area of a sector of this circle with that central angle.

1. $$\pi$$ radians

### Solution

(From Unit 7, Lesson 13.)

### Problem 7

Select all formulas that could be used to find the area of this sector. The angle $$\theta$$ is measured in radians.

A:

$$\frac12 r^2 \theta$$

B:

$$\frac{\theta}{2\pi}\boldcdot \pi r^2$$

C:

$$\frac{\theta}{360}\boldcdot \pi r^2$$

D:

$$\frac{\pi^2}{r}\boldcdot \theta$$

E:

$$\frac{\theta}{2\pi}\boldcdot 2\pi r$$

### Solution

(From Unit 7, Lesson 13.)

### Problem 8

Triangle $$ABC$$ is shown with an inscribed circle of radius 4 units centered at point $$D$$. The inscribed circle is tangent to side $$AB$$ at point $$G$$. The length of $$AG$$ is 6 units and the length of $$BG$$ is 8 units. What is the measure of angle $$B$$?

A:

60 degrees

B:

30 degrees

C:

$$2 \arctan \left(\frac12\right)$$

D:

$$\arctan \left(\frac12\right)$$

### Solution

(From Unit 7, Lesson 7.)

### Problem 9

Select all the true statements.

A:

Angle $$C$$ is 30 degrees.

B:

Side $$AC$$ is 5 units.

C:

Side $$AB$$ is 5 units.

D:

Side $$AC$$ is $$5 \sqrt2$$ units.

E:

Side $$AC$$ is $$10 \sqrt3$$ units.