Reservoir level in a target band

Question

On any given day the water level in a reservoir is equally likely to be anywhere between 2.0 and 6.0 meters. In other words, the level is uniform across a 4.0-meter range.

What is the probability that the level lands between 3.0 and 4.5 meters?

Accepted Answer

For a value spread evenly over an interval, the probability of falling in a target band equals the length of that band divided by the length of the full range. P(	ext{event}) = \frac{	ext{length of favorable band}}{	ext{length of full range}}. The full range runs from 2.0 to 6.0 meters, a width of 6.0 - 2.0 = 4.0 meters. The favorable band runs from 3.0 to 4.5 meters, a width of 4.5 - 3.0 = 1.5 meters. So P(3.0 \le 	ext{level} \le 4.5) = \frac{1.5}{4.0} = \frac{3}{8} = 0.375. Notice the actual numbers on the scale do not matter, only the widths. A 1.5-meter slice out of a 4.0-meter range …

Reservoir level in a target band

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