grid problem (geometry)

The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

Details and assumptions:

>Note: The black squares are not removed with probability 12. Rather, it is given that exactly 30 black squares are removed.

>A square is a neighbour if it is located directly to the left, right, top or bottom of the initial square. Squares that are connected by exactly 1 vertex are not neighbors.

  1. 0
  2. 0
  3. 4
asked by john

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    The squares of a 2×500 chessboard are coloured black and white in the standard alternating pattern. k of the black squares are removed from the board at random. What is the minimum value of k such that the expected number of

    asked by Sarah on May 16, 2013
  2. Mathematics

    The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no

    asked by Steve on June 16, 2013
  3. maths

    The squares of a 3×3 board are randomly coloured black or white. Let W be the number of white squares and B the number of black squares. The expected value of |B−W| can be expressed as ab where a and b are coprime positive

    asked by su on May 9, 2013
  4. maths

    The squares of a 3×3 board are randomly coloured black or white. Let W be the number of white squares and B the number of black squares. The expected value of |B−W| can be expressed as ab where a and b are coprime positive

    asked by hemant on May 8, 2013
  5. math

    I am having trouble understanding how to solve this problem. I found an answer, about 74.2%, but I am not sure if that is correct. Any help would be greatly appreciated! A chess board has 64 squares, 32 white and 32 black, and is

    asked by anonymous on May 25, 2015
  6. IT

    WHY WHEN I SEND A COLOURED DOCUMENT FROM MY HOME COMPUTER VIA WEBMAIL TO MY SCHOOL SITE DOES IT THEN PRINT OUT ON THE SCHOOL PRINTER AS BLACK AND WHITE EVEN THOUGH I CHOOSE THE COLOURED PRINTER 1) is your school printer a color

    asked by REBECCA on November 12, 2006
  7. Math

    Poor Delbert has been asked to do some tiling at home. He doesn't really understand the pattern. Can you help? How many black tiles to white?(1 to every 2) What is the proportion of black tiles to the whole pattern(1/3) What is

    asked by Sameeha on February 6, 2016
  8. Math

    im having a hard time with polynomials it just shows shapes and i dont understand, if somebody could help that would be great :) Which polynomial does the model represent? The picture shows a big black square, 2 white rectangles 1

    asked by Help me please on June 9, 2017
  9. biology urgent

    In mice, a gene controlling coat colour has 2 alleles; B (black) and b (white). A pure breeding black mouse is crossed to a white mouse and all the offspring are black. The offspring are then crossed to white mice. The phenotypes

    asked by alex on February 25, 2013
  10. Math

    A printer takes 50 minutes to print a total of 1200 identical black-and-white posters and 500 identical coloured posters. The same printer takes 1 hour to print 2400 such black-and-white posters. How many such coloured posters can

    asked by chimingbell on May 6, 2018

More Similar Questions