# Contesting for Idiot du Jour

Roger Guay irog at mac.com
Wed Sep 2 22:38:29 EDT 2020

```Your chance to be Genius du Jour:

If I construct 2 concentric circles, one being half the radius of the larger, then simple math shows that the smaller circle has an area ¼ the area of the larger.
Now if I generate a random point within the radius of the larger circle, I should expect that the probability of it landing in the smaller circle to be ¼.
But, I must be doing something wrong because I get ½ !

Here is my script:

on mouseDown

getStuff

end mouseDown

local tR, tTheta, tX0, tY0, tX1, tY1, tTotCount, tL, tLongCount

on getStuff

put item 1 of the loc of grc OuterCircle into tx0

put item 2 of the loc of grc OuterCircle into tY0

put "" into tTotCount

put "" into tLongCount

emptyFlds

end getStuff

on mouseUp

lock screen

repeat 1000

put random(200) into tR -- 200 is half the width of the larger circle

if tR > 1 then

## put random(2*pi) into tTheta1

get random(360)

put it*pi/180 into tTheta1

put tR*cos(tTheta1) into tX1
put tR*sin(tTheta1) into tY1

set the loc of grc Ptgrc to tX0 + tX1, tY0 - tY1 --- grc Ptgrc is a 2 pixle oval

if intersect(grc Ptgrc, grc InnerCircle, "opaque Pixels") then add 1 to tLongCount

end if

end repeat
put tTotCount into fld "totcountFld"

put tLongCount into fld “LongCountFld"

put tLongCount/tTotCount into fld "RatioFld"

unlock screen

end mouseUp

Apparently, this does not generate a random point within the larger circle! Can someone please tell me what’s wrong here?

Thanks,
Roger
```