Question

the tree below shows the sample space of picking a red, purple, or violet marble and rolling a standard number cube during a game. there is an equally likely chance of picking any color. find the probability of each event. now, find the probability of picking a violet marble and rolling anything but a 3. the probability of someone picking a violet marble and rolling anything but a 3 is \\(\frac{\square}{\square}\\).

Explanation:

Step1: Probability of violet marble

There are 3 colors (red, purple, violet), so probability of violet is $\frac{1}{3}$.

Step2: Probability of not rolling a 3

A standard cube has 6 sides. Rolling not a 3 means 5 outcomes (1,2,4,5,6), so probability is $\frac{5}{6}$.

Step3: Multiply the probabilities

Since the events are independent, multiply the two probabilities: $\frac{1}{3} \times \frac{5}{6} = \frac{5}{18}$.

Answer:

$\frac{5}{18}$