Maths Olympiad Prep

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, 2014

Combinatorics Difficulty 1.7 Junior Find the answer Canada

On each spin of the spinner shown, the arrow is equally likely to stop on any one of the four numbers.

Deanna spins the arrow on the spinner twice. She multiplies together the two numbers on which the arrow stops. Which product is most likely to occur?

Pick one

Solutions — 2

Solution 1

We make a chart that lists the possible results for the first spin down the left side, the possible results for the second spin across the top, and the product of the two results in the corresponding cells:

1
2
3
4

1
1
2
3
4

2
2
4
6
8

3
3
6
9
12

4
4
8
12
16

Since each spin is equally likely to stop on 1, 2, 3, or 4, then each of the 16 products shown in the chart is equally likely.

Since the product 4 appears three times in the table and this is more than any of the other numbers, then it is the product that is most likely to occur.

Solution 2

We make a chart that lists the possible results for the first spin down the left side, the possible results for the second spin across the top, and the product of the two results in the corresponding cells:

1
2
3
4

1
1
2
3
4

2
2
4
6
8

3
3
6
9
12

4
4
8
12
16


Since each spin is equally likely to stop on 1, 2, 3, or 4, then each of the 16 products shown in the chart is equally likely.

Since the product 4 appears three times in the table and this is more than any of the other numbers, then it is the product that is most likely to occur.

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