Final answer:
The probability of drawing a red marble and then a yellow marble from Mr. Guo's bag, with replacement, is the product of the individual probabilities for each event. Since the probability of drawing a red marble is 1/15 and the probability of drawing a yellow marble is 3/15, the combined probability is approximately 1.33%, which corresponds to answer choice (D) 1.3%.
Step-by-step explanation:
To find the probability of picking a red marble, replacing it, and then a yellow marble from Mr. Guo's bag, we need to calculate the likelihood of each event independently because after replacing the red marble, the draws are independent events.
The probability of drawing a red marble (P(Red)) from the bag is the number of red marbles divided by the total number of marbles, which is:
P(Red) = ⅓ (1 red marble out of 15 total marbles).
The probability of drawing a yellow marble (P(Yellow)) after the red marble has been replaced is:
P(Yellow) = ⅗ (3 yellow marbles out of 15 total marbles).
Since the marble is replaced after the first draw, the probability of these two events happening in sequence is the product of the individual probabilities:
P(Red then Yellow) = P(Red) × P(Yellow) = ⅓ × ⅗ = ⅓⅗.
Converting this fraction to a percentage gives us:
P(Red then Yellow) = (1/15) × (3/15) = 3/225 = 1/75 = approximately 1.33%.
Thus, the correct answer is (D) 1.3%.