The internet world says this
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12-12-2015, 10:17 AM
RE: The internet world says this
(12-12-2015 09:48 AM)Full Circle Wrote:  Four unit squares are chosen at random on a chessboard. What is the probability that three of them are of one color and the fourth is of opposite color?

Ok, 8²=64


there is black and white so 1/2


1/2*(1/2)^3*64=4

did that wrong one min
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12-12-2015, 10:19 AM
RE: The internet world says this
pass i dont know
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12-12-2015, 10:20 AM
RE: The internet world says this
so we have aaab each individual has a 1/2 being blk or white?
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12-12-2015, 10:21 AM
RE: The internet world says this
so 0.5^4=0.0625
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12-12-2015, 10:23 AM
RE: The internet world says this
The number of ways of choosing 4 squares from 64 is 64C4

The possible split ups as far as color is concerned and the number of ways of selecting the square are listed below:

White = 0, Black = 4, No. of Ways = 32C0×32C4

White = 1, Black = 3, No. of Ways = 32C1×32C3

White = 2, Black = 2, No. of Ways = 32C2×32C2

White = 3, Black = 1, No. of Ways = 32C3×32C1

White = 4, Black = 0, No. of Ways = 32C4×32C0

The number of ways in which 3 squares are of one color and fourth is of opposite color is:

P(A)=2×32C1×32C3

=(2×32)32×31×3032×3

The total number of ways of selecting 4 squares is:

=P(B)=64C4

=64×63×62×612×3×4

The required probability

=P(A)P(B)

=640/1281

or almost exactly 0.5

Verdict is in, you are a poser.

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
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12-12-2015, 10:24 AM
RE: The internet world says this
the answer is 25%
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12-12-2015, 10:27 AM
RE: The internet world says this
1/4=0.25
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12-12-2015, 10:36 AM (This post was last modified: 12-12-2015 12:45 PM by Full Circle.)
RE: The internet world says this
(12-12-2015 10:27 AM)Theorist Wrote:  1/4=0.25

I gave you the correct answer and you insist on a different answer...Facepalm

I think I see the problem here (pun intended).

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
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12-12-2015, 10:39 AM
RE: The internet world says this
(12-12-2015 10:36 AM)Full Circle Wrote:  
(12-12-2015 10:27 AM)Theorist Wrote:  1/4=0.25

I gave you the corret answer and you insist on a different answer...Facepalm

I think I see the problem here (pun intended).

You said pick 4 random squares from a chess board, then asked what it the chance of only one white or only 1 black, so 1/4=0.25


the chance of two white and two black = .5
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12-12-2015, 10:52 AM (This post was last modified: 12-12-2015 11:16 AM by Theorist.)
RE: The internet world says this
φ=1:2

φ/4=0.125:4


and considering a chess board randomly mix the rows, and observe black black black or white white white. in the columns.
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