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
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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.
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.
- \(\pi\) radians
- 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.
\(\frac12 r^2 \theta\)
\(\frac{\theta}{2\pi}\boldcdot \pi r^2\)
\(\frac{\theta}{360}\boldcdot \pi r^2\)
\(\frac{\pi^2}{r}\boldcdot \theta\)
\(\frac{\theta}{2\pi}\boldcdot 2\pi r\)
Solution
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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 \(B\)?
60 degrees
30 degrees
\(2 \arctan \left(\frac12\right)\)
\(\arctan \left(\frac12\right)\)
Solution
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(From Unit 7, Lesson 7.)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.
Solution
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(From Unit 4, Lesson 3.)