MathDB

Adam is playing Minesweeper on a

9\times9

grid of squares, where exactly

\frac13

(or 27) of the squares are mines (generated uniformly at random over all such boards). Every time he clicks on a square, it is either a mine, in which case he loses, or it shows a number saying how many of the (up to eight) adjacent squares are mines.
First, he clicks the square directly above the center square, which shows the number

4

. Next, he clicks the square directly below the center square, which shows the number

1

. What is the probability that the center square is a mine?
Proposed by Adam Bertelli

Problem Statement