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A 5 imes 5 Minesweeper grid has 3 mines. What is the probability of picking a safe square or a mine on the first try?

Computer Science

ScanSolve AI Answer

Step-by-step solution

4 steps

  1. Determine the total number of squares and the number of mines.

    The grid is 5×55 \times 5, so the total number of squares is 5×5=255 \times 5 = 25.
    The image indicates "Mines: 3", meaning there are 3 mines hidden in the grid.

  2. Calculate the number of safe squares.

    The number of safe squares is the total number of squares minus the number of mines.

    Number of safe squares=25−3=22\text{Number of safe squares} = 25 - 3 = 22

  3. Calculate the probability of picking a safe square on the first attempt.

    The probability of picking a safe square is the ratio of safe squares to the total number of squares.

    P(safe square)=Number of safe squaresTotal number of squares=2225P(\text{safe square}) = \frac{\text{Number of safe squares}}{\text{Total number of squares}} = \frac{22}{25}

    As a decimal, this is 0.88. As a percentage, this is 88%88\%.

  4. Calculate the probability of picking a mine on the first attempt.

    The probability of picking a mine is the ratio of mines to the total number of squares.

    P(mine)=Number of minesTotal number of squares=325P(\text{mine}) = \frac{\text{Number of mines}}{\text{Total number of squares}} = \frac{3}{25}

    As a decimal, this is 0.12. As a percentage, this is 12%12\%.

    The probability of picking a safe square on the first attempt is 2225\boxed{\frac{22}{25}} or 88%\boxed{88\%}.
    The probability of picking a mine on the first attempt is 325\boxed{\frac{3}{25}} or 12%\boxed{12\%}.

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