 # One of the wagers in roulette is to bet that the ball will stop on a number that a multiple of 3. If the ball stops on such a number, the player wins double the amount bet. What is the probability of winning this bet? Clifland 2021-08-10 Answered
One of the wagers in roulette is to bet that the ball will stop on a number that a multiple of 3. (The roulette wheel Includes the numbers 0,00and 1 - 36 . and 00 are not considered multiples of 3.) If the ball stops on such a number, the player wins double the amount bet. What is the probability of winning this bet? (Write your answer as a fraction.)

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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 $$\displaystyle={\frac{{{13}}}{{{38}}}}$$