If $x \in[0,5]$, then what is the probability that $x^2-3 x+2 \geq 0$ ?

• Correct answer
  A

  4/5
• B

  1/5
• C

  2/5
• D

  3/5

Solution

$\begin{aligned} & \text { Let } x^2-3 x+2=0 \\ & \Rightarrow x=1,2 \\ & \therefore x^2-3 x+2 \geq 0 \text { for } x \in[0,1] \cup[2,3] \cup[3,4] \cup[4,5] . \\ & \text {It is given that : } \\ & x \in[0,1] \cup[1,2] \cup[2,3] \cup[3,4] \cup[4,5] \\ & \therefore \text { Required probability }=\frac{4}{5}\end{aligned}$

Hence, the correct answer is option: 'A'.