Question

Two real numbers x, y are selected such that $x,yϵ[0,4].$ Then the probability that the selected numbers satisfy the inequation $y^2\le x$ is

• A. $1/2$
• B. $1/3$
• C. $1/4$
• D. $1/5$

Answer 1

The correct option is B $1/3$

Required Probability $=\frac{{\int }_0^4(y{)}_{\text{parabola}}dx}{16}$
$=\frac{{\int }_0^4\sqrt{x}dx}{16}=\frac{16/3}{16}=\frac{1}{3}$