If a real number x is chosen at random in the interval [0,5] and a real number y is chosen at random in the interval [0,6], what is the probability that x < y?
Answers.
A) 2/3  B) 3/5  C) 5/12  D) 7/12  E) 11/15
Since x is in [0,5] and y is in [0,6] we can draw a rectangle in the coordinate plane with vertices (0, 0), (5, 0), (0, 6), and (5, 6).   The points above the line y=x satisfy x &lt; y.   The part of the rectangle below y=x has an area of 12.5   The whole rectangle has an area of 30.   P(x &lt; y) = (30-12.5)/30 = 17.5/30 = 35/60 = 7/12   The answer is 7/12.
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If a real number x is chosen at random in the interval [0,5] and a real number y is chosen at random in the interval [0,6], what is the probability that x < y?