Question

the central angle of sector s is 57°. what is the probability that the spinner does not land on s? simplify your answer and write it as a proper fraction.

Explanation:

Step1: Find the central angle of the non - S region

A full circle has a central angle of \(360^{\circ}\). The central angle of sector S is \(57^{\circ}\), so the central angle of the region where the spinner does not land on S is \(360 - 57=303^{\circ}\).

Step2: Calculate the probability

The probability that the spinner does not land on S is the ratio of the central angle of the non - S region to the central angle of the full circle. So the probability \(P=\frac{303}{360}\).

Step3: Simplify the fraction

We find the greatest common divisor (GCD) of 303 and 360. The GCD of 303 and 360 is 3. Divide both the numerator and the denominator by 3: \(\frac{303\div3}{360\div3}=\frac{101}{120}\).

Answer:

\(\frac{101}{120}\)