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Probability of Coin inside Square Tile

XAT 2018 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

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A coin of radius 3 cm3\text{ cm} is randomly dropped on a square floor full of square shaped tiles of side 10 cm10\text{ cm} each. What is the probability that the coin will land completely within a tile? In other words, the coin should not cross the edge of any tile.

  1. A.

    0.91

  2. B.

    0.5

  3. C.

    0.49

  4. D.

    0.36

  5. E.

    0.16

Answer

E

Explanation

For the coin of radius r=3 cmr = 3\text{ cm} to land completely inside a square tile of side s=10 cms = 10\text{ cm}, its center must be at least 3 cm3\text{ cm} away from each of the 4 edges of the tile.

The valid region for the center of the coin is a smaller square of side length: 10−2(3)=4 cm10 - 2(3) = 4\text{ cm}

Area of valid region=4×4=16 sq. cm\text{Area of valid region} = 4 \times 4 = 16\text{ sq. cm} Total area of a tile=10×10=100 sq. cm\text{Total area of a tile} = 10 \times 10 = 100\text{ sq. cm}

Probability=16100=0.16\text{Probability} = \frac{16}{100} = 0.16

Thus, Option E is correct.

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