Question

mei puts the shapes below into a bucket and asks brian to pick one out.
a. what is the probability that he pulls out a quadrilateral with parallel sides?
b what is the probability that he pulls out a shape with rotation symmetry?

Explanation:

Step1: Count total shapes

There are 6 shapes in total.

Step2: Count quadrilaterals with parallel sides

The rhombus, parallelogram, trapezoid, and square are quadrilaterals with parallel sides. So there are 4 such shapes.
The probability for part a is $\frac{4}{6}=\frac{2}{3}$.

Step3: Count shapes with rotation symmetry

The rhombus, parallelogram, equilateral - triangle, and square have rotation symmetry. So there are 4 such shapes.
The probability for part b is $\frac{4}{6}=\frac{2}{3}$.

Answer:

a. $\frac{2}{3}$
b. $\frac{2}{3}$