Answer
$\dfrac{7}{36}$
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 yellow marble is given by the number of yellow marbles divided by the total number of marbles. That is
\begin{align*}
&
\dfrac{14}{72}
\\\\&=
\dfrac{\cancel{14}^7}{\cancel{72}^{36}}
\\\\&=
\dfrac{7}{36}
.\end{align*}
Hence, the probability of randomly choosing a yellow ball is $
\dfrac{7}{36}
.$