Question

Two numbers x ∈ R and y ∈ R are selected such that x ∈ [ 0 , 4 ] and y ∈ [ 0 , 4 ] . Find the probability that the selected numbers satisfy the inequation y² ≤ x is

Answer 1

Required Probability = \(\frac{\int ^4_0 (y)_{parabola}dx}{16}\)

\(=\frac{\int ^4_0 \sqrt{xdx}}{16}=\frac{16/3}{16}=\frac{1}{3}\)