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Problem 117

Combinatorics Difficulty 1.3 Multiple choice CEMC Pascal · Canada · 2022

A circular spinner is divided into 4 sections, as shown. The
angles at the centre of the circle in the sections labelled Green and
Blue each measure 90∘90^\circ.

An arrow is attached to the centre of the spinner. The arrow is spun
once. What is the probability that the arrow lands on either Red or
Yellow?

Pick one

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Official solution

The total central angle in a circle is 360∘360^\circ.

Since the Green section has an angle at the centre of the circle of
90∘90^\circ, this section corresponds
to $90∘360∘=14$\$\frac{90^\circ}{360^\circ} = \frac{1}{4}\$ of the circle.

This means that when the spinner is spun once, the probability that it
lands on the Green section is 14\frac{1}{4}.

Similarly, the probability that the spinner lands on Blue is also 14\frac{1}{4}.

Since the spinner lands on one of the four colours, the probability that
the spinner lands on either Red or Yellow is $1 - 14−14=12$.\frac{1}{4} - \frac{1}{4} = \frac{1}{2}\$.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.