Question

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

P (Triangle)

Short answer

The probability of choosing a triangle is $\frac{1}{2}$.

Step-by-step solution

Step 1. State the formula.

The formula for the probability of an event is $P\left(E\right)=\frac{n}{T}$, where E denotes the event, P(E) denotes the probability of the event E, n denotes the number of favorable outcomes and T denotes the total number of outcomes.

Step 2. List the given data.

The collection of polygons in the given figure contains 3 triangles, 1 square, 1 rectangle and 1 pentagon.

Step 3. Explanation.

The event is “choosing a triangle”.

The collection of polygons in the given figure contains 3 triangles, 1 square, 1 rectangle, and 1 pentagon.

Since the collection of polygons contains 3 triangles, $n=3$.

The total number of polygons in the collection is $3+1+1+1=6$. Then, $T=6$.

Step 4. Calculate the probability.

Put $E:\mathrm{triangle}$, $n=3$and $T=6$in $P\left(E\right)=\frac{n}{T}$to get,

$$\begin{gathered} P\left(\mathrm{triangle}\right)=\frac{3}{6} \\ =\frac{1}{2} \end{gathered}$$

So,

$P\left(\mathrm{triangle}\right)=\frac{1}{2}$

The probability of choosing a triangle is $\frac{1}{2}$.