Thread: Question on total probability formula

Hi, my question is:
Two different squares are selected at random on an 8 x 8 chessboard. What is the probability that they share a common boundary (i.e. that htey have an edge in common, not just a single corner)?

For this question, it says I'm supposed to use the total probability formula. Any help would be greatly appreciated

Hey sakuraxkisu.

I'm not familiar with that term, but you could point out what the total probability formula is in your book/lecturer/whatever?

Hello, sakuraxkisu!

I too have never heard of the total probability formula.
Could you explain it?

Two different squares are selected at random on an 8 x 8 chessboard.
What is the probability that they share a common boundary?

Selecting 2 of the 64 squares, there are: . outcomes.

Consider placing a domino in a row: .
There are 7 possible positions.
On the entire board, there are ways
. . to place a domino horizontally.

Consider placing a domino in a column.
There are 7 possible positions.
On the entire board, there are ways
. . to place a domino vertically.

Hence, there are pairs of adjacent squares.


The probability is; .

In my lecture notes, it says that the formula is:

Assuming that form a partition of the sample space and that form a partition of A.

I got the same answer as you Soroban, although my method was slightly different. I think what confused me most was how this formula could be used in the question. Thank you anyway though