A Minesweeper Probability Question

The above picture is the bottom-left corner of a Minesweeper game. We are given that there are 4 total bombs among the 9 untouched squares (1 light blue and 8 blue squares excluding those squares with a red flag).

Find the probability that the highlighted (light blue) square is a bomb. Assume that each possible arrangement of bombs is equally likely (with "possible" meaning it satisfies the given number clues).

Notes: (in case you're unfamiliar with Minesweeper)

  • The number on a white square represents the number of bombs adjacent to that square (including diagonally). These are squares which do not each have a bomb on them.

  • A red flag indicates a square where we already know there is a bomb.

  • Blue squares without a flag are "untouched," including the highlighted one. We are not given whether they have a bomb or not.


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