Multiple choice

A circle with diameter 15 cm is drawn somewhere on a rectangular piece of paper with length 50 cm and width 40 cm. This paper is kept horizontal on table top and a die, very small in size, is dropped on the rectangular paper without seeing towards it, if the die falls and lands on the paper only, find the probability that it will fall and land outside the circle but inside the rectangle.

  1. 0.56

  2. 0.82

  3. 0.42

  4. 0.91
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Area of rectangle = 50 * 40 = 2000. Area of circle = pi * r^2 = 3.14 * (7.5)^2 = 3.14 * 56.25 = 176.625. Probability of landing inside the circle = 176.625 / 2000 = 0.0883. Probability of landing outside = 1 - 0.0883 = 0.9117, which rounds to 0.91.

AI explanation

Using the geometric probability method, the area of the rectangle is 50 multiplied by 40, giving 2000 square centimeters, and the area of the circle is pi times the radius squared, which is 3.14 times 7.5 squared, or about 176.625 square centimeters. The probability of the die landing outside the circle is (2000 minus 176.625) divided by 2000, which equals 0.91.

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