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Disk Toss on a Grid (Posted on 2016-07-08) Difficulty: 3 of 5
A disk that is 1 cm in diameter is tossed onto a 6x6 grid of squares with each square having side length 1.25 cm.

A disk is in a winning position if no part of it touches or crosses a grid line- otherwise it is in a losing position

The disk is tossed and it lands in a random position so that no part of it is outside the grid.

What is the probability that the disk is in a winning position?

No Solution Yet Submitted by K Sengupta    
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Solution solution | Comment 1 of 4
The grid is 7.5x7.5 cm and the center of the disk cannot be within .5 cm of the edge of the grid and so is limited to a 6.5x6.5 area.

There are 16 central  1.25x 1.25 squares, in which there is a .25x.25 area in which the tossed disk's center can fall and win. In fact each of the 36 squares of the grid contains this .25x.25 possible area for a win. The winning area of the board is 2.25 cm^2.

2.25/(6.5*6.5) = 2.25/42.25 = 9/169 ~= 0 .0532544378698225

is the probability of not falling on a line given that it has fallen completely within the grid.

Correcting original post where I had 36*.25^2 equalling 6.25; looks like I had multiplied by 100 instead of 36.

Edited on July 8, 2016, 8:51 pm
  Posted by Charlie on 2016-07-08 11:17:15

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