A real number x is chosen at random such that -2 < x < 5. What is the probability that x^{2} < 2?

A real number x is chosen at random such that -2 < x < 5. What is the probability that x^2 < 2?

if x^2 <2

then

\(-\sqrt2

The distance between these is \(2\sqrt2\)

The distance between -2 and 5 is 7

so

The prob will be \(\frac{2\sqrt2}{7}\)