Lesson 2

Playing with Probability

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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:

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

Solution

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Problem 2

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

A:

THE

B:

BEST

C:

SNEEZE

D:

FREES

E:

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?

Spinner with 5 sections. Sections R, G and Y each make up one fourth of spinner. Sections P and B each 1 eighth of spinner.
A:

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

B:

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

C:

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

D:

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

Solution

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(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.

Spinner with 6 equal sections, labeled A, B, C, D, E and F.

Solution

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(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
  2. 3 radians

Solution

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(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 circle with shaded sector with a central angle labeled theta and radius r.
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

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(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 \(B\)?

Triangle ABC with a circle inside with center D. Dashed lines from D to outside of circle, one labeled 4. AG = 6. BG = 8.
A:

60 degrees

B:

30 degrees

C:

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

D:

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

Solution

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(From Unit 7, Lesson 7.)

Problem 9

Select all the true statements. 

Right triangle ABC. Angle A = 90 degrees. Angle B = 60 degrees. Side BC= 10 units. 
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.

Solution

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(From Unit 4, Lesson 3.)