Coin Toss experiment

[Anonymous No.9941510]

Okay /sci/

I have a little problem for you.

>You have a Chessboard with squares having 3 inches height and width
>You have a round coin with 2 inches diameter
>You throw the coin. Each time it lands without touching the edge of a square you gain 90cent. Otherwise you lose 10

Would you throw the coin?

[Anonymous No.9941512]

>>9941510
If it touches multiple edges does it stack? (4 edges, 40c) If so no. If no, yes I do throw

[Anonymous No.9941516]

>>9941510
Calculate the safe are
Calculate the not-safe area
If sa > n-sa you toss the coin

[Anonymous No.9941519]

>>9941516
But payback in 9x the loss so you can still get a good return even if the safe area is small, it would just be more work to calculate what that limit is

[Anonymous No.9941525]

>>9941510
Expected value is positive, which is probably what your homework expects you to say.

>>9941516
lol how is the Riemann hypothesis even hard dude just figure out where the zeroes are

[Anonymous No.9941557]

>>9941510
I don't bother because winning 90 cents is not worth bothering with.

Now I DO buy lottery tickets from time to time. The odds are, og course, terrible -- but what I put at risk, I'll never miss, and if I DO happen to win it'll be life-changing.

[Anonymous No.9941605]

pick a random center of a circle for x (0;3) and y (0;3).
if Xcenter<=1, you lose ==> 1/3 chance
if Xcenter>=2, you lose ==> 1/3 chance

if Xcenter>=1&&<2 AND Ycenter<=1, you lose ==> 1/9 chance
if XCenter>=1&&<2 AND Ycenter>=2, you lose ==> 1/9 chance

in total you lose 1/3+1/3+1/9+1/9=8/9 times, which is 88,89%.

there might be some autism involved with depending on how the edges of the chessboard itself is handled which i wont bother with.

[Anonymous No.9941636]

assumption: it must land entirely within the confines of the chessboard, no landing with part of the coin extending beyond the edge
left edge: 0 to 1 inch safe, 1/3rd of available space is safe
1/3rd of the space is safe horizontally, 1/3rd vertically
1/9th space in total is safe

1/9*90-8/9*10=1.111
the expected value is just slightly positive but it's so slightly so that i dunno i'd rather not waste time on it

[Anonymous No.9941649]

>>9941636
actually i think my assumption kills that calculation, i'm overestimating the available unsafe space

[Anonymous No.9942474]

>>9941510
First, it should be recognized that if the coin must land inside the chessboard, then the problem can be simplified without a loss of generality to the single square on the chessboard which the center of the coin is contained in. From this, the problem becomes a question of the probably the center of the coin lands within a given square such that this point is at least 1 inch away from the sides of the square. This "safe" area, which is a 1 diameter circle whose center is also at the center of the square, can be realized by considering that the shortest distance from the edge of the 3x3 inch square to its center is 1.5 inches (this fact can definitely be proved by some simple geometry I do not have the patience to rigorously describe). So the probability will be the area of this "safe" circle divided by the total area of the square. The area of the circle is pi/4 in^2, the area of the square is 9 in^2, so the probability is pi/36, or about 8.7%

This is a first crack at the problem given on first glance, and the probability seems rather low, so I would not be surprised if the answer is incorrect in approach. However, the argument seems to be logically sound unless a certain probability rule was missed somewhere

[Anonymous No.9942492]

>>9941510
>throw coin so that it doesn't land on the board
>gain free 90 cents

[Anonymous No.9942535]

>>9942474
quick correction to this post, the safe area within a square for the center to land is a 1x1 square in the center of the square, not a circle of radius 1/2, which confirms the probability is 1/9

[Anonymous No.9942568]

>>9941510
Yes, just throw the coin outside the chessboard for infinite free money.