# Probability

**Algebra**Level 5

Let \(P(x) = x^2 - 3x - 9\). A real number \(x\) is chosen at random from the interval \(5 \le x \le 15\). The probability that \(\lfloor\sqrt{P(x)}\rfloor = \sqrt{P(\lfloor x \rfloor)}\) is equal to \(\frac{\sqrt{a} + \sqrt{b} + \sqrt{c} - d}{e}\), where \(a, b, c, d\), and \(e\) are positive integers. Find \(a + b + c + d + e\).