Question

Two real numbers are selected from the closed interval [0,4] say x and y.
What is the probability that the selected numbers sastisfy y^2<=x

Answer 1

We are choosing points (x,y) in the square [0,4] x[0,4] which has an area of 16

Answer 2

To satisfy the inequality (x,y) should be chosen under the curve
\[
y= \sqrt x
\]
The area under this curve is
\[
\int_0^4 \sqrt x dx=\frac {16}3
\]

Answer 3

Hence the answer is
\[

\frac {\frac {16}3}
{16}=\frac 1 3
\]

Answer 4

awesome!thanks :D