Question

the central angle of sector f is 171°. the central angle of sector e is 45°. what is the probability that the spinner lands on f or e? write your answer as a fraction or decimal. do not round.

Explanation:

Step1: Find the sum of central angles of sector \(F\) and \(E\)

The sum of central angles of sector \(F\) and \(E\) is \(171^{\circ}+ 45^{\circ}=216^{\circ}\)

Step2: Use the probability formula for a spinner (probability \(P=\frac{\text{Central angle of the region}}{\text{Total central angle of the circle}}\))

Since the total central angle of a circle is \(360^{\circ}\), the probability \(P = \frac{216}{360}\)
Simplify \(\frac{216}{360}\):
\(\frac{216\div72}{360\div72}=\frac{3}{5}=0.6\)

Answer:

\(0.6\) or \(\frac{3}{5}\)