probability

[ritu]

hey guys help me out wid these questions.......
if the squares of a 8*8 chess board are painted either red or black at random....
1.what is the pr that not all squares in any column are alternating in color?
2.wat's the pr that chess board contains equal number of red and black squares?
3.wat's the pr that all squares in any column are of same color and alternating color in any row?
pls reply

[duck]

Hi Ritu.. :)

1) Probability that not all squares in any column are alternating in color= [1-1/2^7]^8
{First, try to find out the probability in which you can color a column such that they alternate in color}

2)Probability that chess board contains equal number of red and black squares = 64!/32!*32!*2^64
{Find out the favorable number of cases}

3)Probability that all squares in any column are of same color and alternating color in any row= 1/2^63
{There are only two ways in this case}


Note: Do the same problem in case of 2*2 or 4*4 chessboard.


:)

[ritu]

4hey thanks a lot duck...ur a genius:)))))

[ritu]

hey by the way duck....could you guide how did you prepare for eco entrances....,as in on seeing a question the method of solving doesnt strike me instantly.....i have to think over it a lot.....and which books do you practice for micro and stats???????????
pls reply

[duck]

Hi Ritu.. :)

That's a good thing if you could solve a question even if it takes a lot of time...it shows you don't give up easily and try your best to do it.. Keep up this spirit.. :)
Do a lot of problem solving and continue the thinking process.


For books, refer the following link>
http://economicsentrance.weebly.com/books.html