Question

carmen had 8 green marbles, 6 red marbles, and 2 yellow marbles in a bag. she pulled a marble from the bag at random and then put it back. then she asked her brother to pull a marble from the bag at random. what is the probability that carmen chose a green marble and her brother chose a red one? write your answer as a fraction or decimal. do not round.

Explanation:

Step1: Calculate total number of marbles

Total marbles = Green + Red + Yellow = \(8 + 6 + 2 = 16\)

Step2: Probability Carmen picks green

Probability (Carmen green) = \(\frac{\text{Number of green marbles}}{\text{Total marbles}} = \frac{8}{16} = \frac{1}{2}\)

Step3: Probability brother picks red

Probability (Brother red) = \(\frac{\text{Number of red marbles}}{\text{Total marbles}} = \frac{6}{16} = \frac{3}{8}\)

Step4: Multiply the two probabilities (independent events)

Since the events are independent (marble is put back), the combined probability is \(\frac{1}{2} \times \frac{3}{8} = \frac{3}{16}\) (or \(0.1875\))

Answer:

\(\frac{3}{16}\) (or \(0.1875\))