standard_description: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
problem_activity: Problem 1
At a particular diner, everyone drinks coffee. However, some people drink their coffee with sugar, some with cream, some with both, and some with neither.
Describe the coffee preferences of the 30 people in the diner in the Venn diagram below. Be sure to label the circles appropriately.
10 people just like cream in their coffee.
13 people like sugar in their coffee; 8 of these people also like cream.
7 people like neither cream nor sugar in their coffee.
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Problem 2
Below is a diagram that shows all of the members of the student council at a particular high school. Each member is represented by a labeled point. The students that are in circle “
$$J$$
” are juniors and the students in circle “
$$M$$
” are male.
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Find
$$P(J)$$
.
Find
$$P(M)$$
.
Find
$$P(J \space and \space M)$$
.
Find
$$P(J \space or \space M)$$
.
Why does
$$ P(J \space or \space M)≠P(J)+P(M)$$
? Design a formula to calculate
$$P(J \space or \space M)$$
using any of the probability found in (a) through (c).


aligns: no