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. start by finding the probability of someone picking a purple marble and rolling an even number. the probability of someone picking a purple marble and rolling an even number is \\(\frac{square}{square}\\).

Explanation:

Step1: Probability of picking purple

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

Step2: Probability of rolling even

A standard number cube has numbers 1 - 6. Even numbers are 2, 4, 6 (3 numbers), so probability of rolling even is $\frac{3}{6}=\frac{1}{2}$.

Step3: Multiply probabilities

Since the events are independent, multiply the two probabilities: $\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$.

Answer:

$\frac{1}{6}$