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CEMC Gauss (Grade 7), 2017

Combinatorics Difficulty 1.6 Junior Find the answer Canada

A circular spinner is divided into 20 equal sections, as shown.

An arrow is attached to the centre of the spinner. The arrow is spun once. What is the probability that the arrow stops in a section containing a number that is a divisor of 20?

Pick one

Solution

The positive divisors of 20 are: $1,2,4,5,10,20$ .

Of the 20 numbers on the spinner, 6 of the numbers are divisors of 20.

It is equally likely that the spinner lands on any of the 20 numbers.

Therefore, the probability that the spinner lands on a number that is a divisor of 20 is $\frac{6}{20}$ .

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