Answer
$\dfrac{25}{36}$
Work Step by Step
With $24$ green marbles, $22$ blue marbles, $14$ yellow marbles, and$12$ red marbles, the total number of marbles is
\begin{align*}\require{cancel}
&
24+22+14+12
\\&=
72
.\end{align*}
The probability of getting a not blue marble is given by the number of green, yellow and red marbles divided by the total number of marbles. That is
\begin{align*}
&
\dfrac{24+14+12}{72}
\\\\&=
\dfrac{50}{72}
\\\\&=
\dfrac{\cancel{50}^{25}}{\cancel{72}^{36}}
\\\\&=
\dfrac{25}{36}
.\end{align*}
Hence, the probability of randomly choosing a not blue ball is $
\dfrac{25}{36}
.$