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2012 AMC 10A Problem 20

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2012 AMC 10A Problem 20AMC 10 Step by Step
Name:                             Date: September 13, 2026
Basic Probability · difficulty 4 of 5 · about 7 min · position P16-20

A 3×33 \times 3 square is partitioned into 99 unit squares. Each unit square is painted either white or black with each color being equally likely, chosen independently and at random. The square is then rotated 90 ∘90\,^{\circ} clockwise about its center, and every white square in a position formerly occupied by a black square is painted black. The colors of all other squares are left unchanged. What is the probability the grid is now entirely black?

  1. A)

    49512\frac{49}{512}

  2. B)

    764\frac{7}{64}

  3. C)

    1211024\frac{121}{1024}

  4. D)

    81512\frac{81}{512}

  5. E)

    932\frac{9}{32}

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