Question

Two numbers (x, y) are selected at random from the interval [0, 1]. (a) find the probability that the pair of numbers are outside the unit circle. (b) find the probability that 3y > x.

Answer 1

A) The area of a square of side 1 that is outside a circle of radius 1 is (1 -π/4), so the probability of interest is
.. p(outside unit circle) = 1 - π/4


b) The sets of numbers such that 3y>x is fill an area that is 5/6 of all sets of numbers (x, y) in the interval [0, 1].
.. p(3y > x) = 5/6