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.

Question

Mathematics

Francis

8 July, 10:58

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.

+1

Answers (1)

Know the Answer?

Mara Payne · 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