If `x in [0,5]`, then what is the probability that `x^2 - 3x + 2 > 0`

Options

A. `(4)/(5)`
B. `(1)/(5)`
C. `(2)/(5)`
D. `(3)/(5)`

Answer

A

Explanation

Let `x^(2)-3x+2=0`
`Rightarrowx=1,2`
`therefore x^(2)-3x+2 ge 0 "for "x in [0,1' cup [2,3] cup [3,4\] cup [4,5]`
It is given that
`x in [0,1] cup [1,2] cup [2,3] cup[ 3,4]cup[4,5]`
`therefore "Required Ratio"=(4)/(5)`