Final answer:
The probability of selecting at least two blue marbles when choosing three marbles without replacement is 0.385.
Step-by-step explanation:
To find the probability that the selected marbles contain at least two blue marbles, we need to consider two cases: (1) selecting two blue marbles and one red marble, and (2) selecting three blue marbles.
Case 1: Selecting two blue marbles and one red marble:
The number of ways to select two blue marbles from six blue marbles is C(6,2) = 15. The number of ways to select one red marble from eight red marbles is C(8,1) = 8. The total number of ways to select three marbles is C(14,3) = 364. Therefore, the probability of selecting two blue marbles and one red marble is 15 * 8 / 364 = 120 / 364 = 0.33 (rounded to two decimal places).
Case 2: Selecting three blue marbles:
The number of ways to select three blue marbles from six blue marbles is C(6,3) = 20. The total number of ways to select three marbles is C(14,3) = 364. Therefore, the probability of selecting three blue marbles is 20 / 364 = 0.055 (rounded to three decimal places).
To find the overall probability of selecting at least two blue marbles, we need to add the probabilities from both cases: 0.33 + 0.055 = 0.385 (rounded to three decimal places).