Waterloo University Problem-II

Probability Level 2

A 10 10 by 10 10 grid is created using 100 100 points, as shown. Point P P is given. One of the other 99 99 points is randomly chosen to be Q . Q. What is the probability that the line segment P Q PQ is vertical or horizontal?

2 89 \frac{2}{89} 2 99 \frac{2}{99} 2 33 \frac{2}{33} 2 11 \frac{2}{11} 1 100 \frac{1}{100}

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

Mahdi Raza
Feb 20, 2020

1 Helpful 0 Interesting 1 Brilliant 0 Confused
David Vreken
Sep 16, 2018

Out of the 99 99 points, 18 18 points (circled below) can be chosen to make P Q PQ vertical or horizontal.

The probability is therefore 18 99 = 2 11 \frac{18}{99} = \boxed{\frac{2}{11}} .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Thank you, nice solution.

Hana Wehbi - 2 years, 8 months ago

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