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 = \(8 + 6+2=16\)

Step2: Calculate probability of Carmen choosing green marble

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

Step3: Calculate probability of brother choosing red marble

Since marble is put back, total marbles remain 16. Probability \(P(\text{red})=\frac{\text{Number of red marbles}}{\text{Total marbles}}=\frac{6}{16}=\frac{3}{8}\)

Step4: Calculate combined probability

Since the two events are independent (marble is replaced), use \(P(A\cap B)=P(A)\times P(B)\). So \(P(\text{green and red})=\frac{1}{2}\times\frac{3}{8}=\frac{3}{16}\)

Answer:

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