# What is geometric probability? Please compare it to binomial distribution and provide an everyday example.Satistics - having trouble distinguishing when the different probabilities should be used.

samhouston | Middle School Teacher | (Level 1) Associate Educator

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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.