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?
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
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