21abhirup i hav one doubt here , while taking the squares why you have not taken squares which dont hav 2 red and 2 black squares, shouldnt they be included in probality finding???
The square of a 8*8 chessboard are randomly painted either red or black,what is the probability that a randomly chosen 2*2 square contains 2 black and 2 red squares?
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6 Answers
13the squares maybe painted thus
RR RB RB BB BR BR
BB BR RB RR BR RB
6 ways....
each square has same probability..i.e...1/2.... of being painted red or black.
2113the board is painted randomly...so a 2*2 square chosen can have any random pattern...it does not depend upon from where the 2*2 square was chosen...
1thats what i thought initially (6/16) but the answer is something like \frac{2^{8}-1}{2^{63}}