1. Tardigrade
  2. Question
  3. Mathematics
  4. If x ∈ [0, 8], the probability that x2 - 8x + 12 ge 0 is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $x \in [0, 8]$, the probability that $x^2 - 8x + 12 \ge 0$ is

Probability - Part 2

Solution:

image
Length of interval $= 8 - 0 = 8$
Also $(x - 2)(x - 6) \ge 6$
Using Wavy curve method, we get
$ x \le 2 $ or $ x \ge 6$
$\Rightarrow $ Interval length for favourable points ,br> $ = 2 - 0 + ( 8 - 6) = 4$
$\therefore $ Required probability $ = \frac{4}{8} = 1/2$
Short Cut Method :
$x^2 - 8x + 12 \ge 0$
$\Rightarrow (x - 2)( x - 6) \ge 0$
$\Rightarrow x \le 2$ or $ x \ge 6$
$\therefore $ Required probability $ = \frac{\int\limits_0^2 dx + \int\limits_6^8 dx}{\int\limits_0^8 dx} $
$= \frac{2 + 2}{8} = 1/2$