CEMC Pascal, 2022

Combinatorics Difficulty 1.3 Junior Find the answer Canada

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 $90^\circ$ .

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

Solution

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

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

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

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

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

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