Mixing
Quarter-circle Tiles
I have $99$ identical square tiles, each with a quarter-circle drawn on it like this:
[asy]
size(1.5cm);
draw(Arc((2,0),1,90,180),red+1);
draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0));
[/asy]
When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form?
I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it.
expected-value
asked Nov 20 '18 at 15:03
6minecraftninja
12
add a comment |
I have $99$ identical square tiles, each with a quarter-circle drawn on it like this:
[asy]
size(1.5cm);
draw(Arc((2,0),1,90,180),red+1);
draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0));
[/asy]
When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form?
I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it.
expected-value
asked Nov 20 '18 at 15:03
6minecraftninja
12
Duplicate: math.stackexchange.com/questions/905673/…
– fahrbach
Nov 20 '18 at 15:19
add a comment |
I have $99$ identical square tiles, each with a quarter-circle drawn on it like this:
[asy]
size(1.5cm);
draw(Arc((2,0),1,90,180),red+1);
draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0));
[/asy]
When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form?
I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it.
expected-value
asked Nov 20 '18 at 15:03
6minecraftninja
12
I have $99$ identical square tiles, each with a quarter-circle drawn on it like this:
[asy]
size(1.5cm);
draw(Arc((2,0),1,90,180),red+1);
draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0));
[/asy]
When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form?
I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it.
expected-value
expected-value
asked Nov 20 '18 at 15:03
6minecraftninja
12
asked Nov 20 '18 at 15:03
6minecraftninja
12
asked Nov 20 '18 at 15:03
6minecraftninja
12
asked Nov 20 '18 at 15:03
6minecraftninja
12
asked Nov 20 '18 at 15:03
6minecraftninja
12
12
Duplicate: math.stackexchange.com/questions/905673/…
– fahrbach
Nov 20 '18 at 15:19
add a comment |
Duplicate: math.stackexchange.com/questions/905673/…
– fahrbach
Nov 20 '18 at 15:19
Duplicate: math.stackexchange.com/questions/905673/…
– fahrbach
Nov 20 '18 at 15:19
Duplicate: math.stackexchange.com/questions/905673/…
– fahrbach
Nov 20 '18 at 15:19
add a comment |
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Duplicate: math.stackexchange.com/questions/905673/…
– fahrbach
Nov 20 '18 at 15:19