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 the total number of marbles

The total number of marbles is \(8 + 6+2=16\) marbles.

Step2: Calculate the probability of Carmen choosing a green marble

The probability of choosing a green marble \(P(G)=\frac{\text{Number of green marbles}}{\text{Total number of marbles}}=\frac{8}{16}\).

Step3: Calculate the probability of her brother choosing a red marble

The probability of choosing a red marble \(P(R)=\frac{\text{Number of red marbles}}{\text{Total number of marbles}}=\frac{6}{16}\).

Step4: Calculate the combined probability

Since the two events (Carmen picking a marble and her brother picking a marble) are independent (because she puts the marble back), we use the formula for the probability of independent events \(P(A\cap B)=P(A)\times P(B)\). So \(P = \frac{8}{16}\times\frac{6}{16}\).

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Answer:

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