Math Probability And Area Problem 9-10th Grade

You can use a technique known as Monte-Carlo integration. In that technique you use a random number generator based upon the height and width of the rectangle to generate a Cartesian point (h0,w0). Then you plot that point on the rectangle and determine if it is inside or outside the bubble.

Repeat this process a number of times. Then count the number if times the point is inside the bubble and divide that by the total number of points generated.

This number is the probability of a point in the rectangle being in the bubble. A probability that becomes more and more accurate as you generate more random points.

The area of the irregular bubble is then determined by multiplying this probability by area of the rectangle.

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