# 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?

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

\(\frac{1}{6}\)

\(\frac{2}{4}\)

\(\frac{2}{6}\)

### Solution

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### Problem 2

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

THE

BEST

SNEEZE

FREES

SPEECH

### Solution

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### 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.

### Solution

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### Problem 4

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

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

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

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

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

### Solution

### 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

### 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.

- \(\pi\) radians
- 3 radians

### Solution

### Problem 7

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

\(\frac12 r^2 \theta\)

\(\frac{\theta}{2\pi}\boldcdot \pi r^2\)

\(\frac{\theta}{360}\boldcdot \pi r^2\)

\(\frac{\pi^2}{r}\boldcdot \theta\)

\(\frac{\theta}{2\pi}\boldcdot 2\pi r\)

### Solution

### 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 \(B\)?

60 degrees

30 degrees

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

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

### Solution

### Problem 9

Select **all **the true statements.

Angle \(C\) is 30 degrees.

Side \(AC\) is 5 units.

Side \(AB\) is 5 units.

Side \(AC\) is \(5 \sqrt2\) units.

Side \(AC\) is \(10 \sqrt3\) units.