Q10 - Algebra 1

Question

One of the polygons below is chosen at random. Find each probability.

P (more than 2 right angles)

Step-by-Step Solution

Answer

The probability of getting a polygon that has more than 2 right angles is $\frac{1}{3}$.

Step 1. Count the numbers of polygons with more than 2 right angles.

Note that a polygon with more than 2 right angles is either a square or a rectangle.

 

Among the given polygons there are 2 polygons that are either a square or a rectangle, i.e. have more than 2 right angles.

Step 2. Apply the basic formula for probability.

The probability of an event is given by the following formula:

$\mathrm{Probability} \mathrm{of} \mathrm{an} \mathrm{outcome}=\frac{\mathrm{number} \mathrm{of} \mathrm{favorite} \mathrm{outcome}}{\mathrm{total} \mathrm{outcome}}$

Step 3. Write the given information.

The total number of figures is 6.

 

The number of favorite outcomes is 2 since there are four figures that are not quadrilaterals among the given figures.

Step 4. Description of step.

Substitute the value of the number of favorite outcomes and total outcomes in the formula for probability.

$$\begin{gathered} \mathrm{P}\left(\mathrm{More} \mathrm{that} 2 \mathrm{right} \mathrm{angles}\right)=\frac{\mathrm{number} \mathrm{of} \mathrm{favorite} \mathrm{outcome}}{\mathrm{total} \mathrm{outcome}} \\ =\frac{2}{6} \\ =\frac{1}{3} \end{gathered}$$

Hence, the probability of getting a polygon that has more than 2 right angles is $\frac{1}{3}$.