The probability that a point chosen at random lies in the shaded region is 0.28
<h3>Calculating the area of a shaded region and probability</h3>
From the question, we are to find the probability that a point chosen at random lies in the shaded region.
The shaded region is a triangle.
The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle
First, we will calculate the unknown side of the triangle
Let the unknown side be x.
Then, from the <em>Pythagorean theorem</em>, we can write that
12² = 6² + x²
144 = 36 + x²
x² = 144 - 36
x² = 108
x = √108
x = 6√3
From formula,
Area of a triangle = 1/2 × base × height
Area of the triangle = 1/2 × 6 × 6√3
Area of the triangle = 18√3 square units
Now, we will determine the area of the circle
Area of a circle = πr²
Where r is the radius
From the given information,
Diameter of the circle = 12
But,
Radius = Diameter / 2
Therefore,
r = 12/2
r = 6
Thus,
Area of the circle = 3.14 × 6²
Area of the circle = 113.04 square units
Now,
The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04
The probability that a point chosen at random lies in the shaded region = 0.2758
The probability that a point chosen at random lies in the shaded region ≈ 0.28
Hence, the probability is 0.28
Learn more on Calculating area of a shaded region here: brainly.com/question/23629261
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