Selecting Marbles A bag contains 9 red marbles, 5 white marbles, and 7 blue marbles. Randomly choose two marbles, one at a time, and without replacement. Find the following. Enter your answers as fractions or decimals rounded to three decimal places. Part: 0 / 3 Part 1 of 3 (a) The probability that the first marble is red and the second is white p (first red and second white)

Answer: To find the probability that the first marble is red and the second is white, you can use the principle of conditional probability. First, find the probability that the first marble drawn is red: Probability(First marble is red) = (Number of red marbles) / (Total number of marbles) Probability(First marble is red) = 9 / (9 + 5 + 7) = 9 / 21 = 3 / 7 Now, since we're drawing without replacement, there are now 20 marbles left in the bag, with 8 of them being red and 5 being white. Next, find the probability that the second marble drawn (after the first was red) is white: Probability(Second marble is white) = (Number of white marbles) / (Total number of marbles left) Probability(Second marble is white) = 5 / 20 = 1 / 4 Now, use the multiplication rule for independent events since the outcome of the first draw doesn't affect the second draw: Probability(First red and second white) = Probability(First marble is red) * Probability(Second marble is white) Probability(First red and second white) = (3 / 7) * (1 / 4) Now, calculate the product: Probability(First red and second white) = (3 / 7) * (1 / 4) = 3 / 28 ≈ 0.107 So, the probability that the first marble is red and the second marble is white is approximately 0.107 when rounded to three decimal places.