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Geometric probability refers to the probability of an area rather than a number. Geometric probability compares the size of the favorable area to the total area. It is usually written as a fraction, however it can also be given as a decimal or percent.
Suppose a rectangular pool is surrounded by a deck and a fence. The pool is 30 ft long and 15 ft wide. The deck is a consistent width around the pool. If a baseball is hit into the fenced area, what is the probability that the baseball will land in the pool?
Allow x to represent the width of the deck.
The favorable area is the area of the pool. 30 * 15 = 450 sq ft
The total area is the area of the pool plus the additional area of the deck.
total length as a binomial: 30 + x + x = 2x + 30
total width as a binomial: 15 + x + x = 2x + 15
total area: (2x + 30)(2x + 15) = 4x^2 + 90x + 450
The geometric probability of the ball landing in the pool is:
450 / (4x^2 + 90x + 450)
If you know the width of the deck, you can get a numerical answer. For example, if the deck is 6 ft wide...
450 / (4 * 6^2 + 90 * 6 + 450)
450 / 1134 `~~` 0.3968 or about 40%.
I hope this helped.
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