what is the probability of picking a green marble and rolling a three? write your answer as a fraction or a…

Explanation:

Step1: Calculate the probability of picking a green marble.

From the image, there are 2 green marbles and 6 purple marbles, making a total of $2+6=8$ marbles. The probability of picking a green marble is the number of green marbles divided by the total number of marbles. $$P(\text{green marble}) = \frac{\text{Number of green marbles}}{\text{Total number of marbles}} = \frac{2}{8} = \frac{1}{4}$$

Step2: Calculate the probability of rolling a three on a standard die.

A standard die has 6 faces, numbered 1, 2, 3, 4, 5, 6. Each outcome is equally likely. The probability of rolling a three is 1 out of 6. $$P(\text{rolling a three}) = \frac{1}{6}$$

Step3: Calculate the combined probability of both independent events.

Since picking a marble and rolling a die are independent events, the probability of both events occurring is the product of their individual probabilities. $$P(\text{green marble and rolling a three}) = P(\text{green marble}) \times P(\text{rolling a three})$$ $$P(\text{green marble and rolling a three}) = \frac{1}{4} \times \frac{1}{6} = \frac{1 \times 1}{4 \times 6} = \frac{1}{24}$$

Answer:

1/24