Step 1

It is given that in a roulette, if ball stops on a number, which is a multiple of 3, the player wins the bet.

Step 2

Total number of outcomes,

\(\left\{0,00\ and\ 1-36\right\} \Rightarrow 38\)

Favourable out comes,

\(\left\{0,3,6,9,12,15,18,21,24,27,30,33,36\right\} \Rightarrow 13\)

Probability of winning \(\displaystyle={\frac{{\text{Favourable out comes}}}{{\text{Total outcomes}}}}\)

\(\displaystyle\Rightarrow{\frac{{{13}}}{{{38}}}}\)

Hence probability of winning \(\displaystyle={\frac{{{13}}}{{{38}}}}\)