Final answer:
To calculate the probability of drawing the desired marbles in succession without replacement, consider the total number of marbles and specific colors. For each option, multiply the probabilities of drawing the desired marbles at each step.
Step-by-step explanation:
To calculate the probability of drawing the desired marbles in succession without replacement, you need to consider the total number of marbles and the specific colors you want to draw. Let's go through each option:
a. 2 white marbles and 1 red marble: There are 7 white marbles and 8 red marbles in the box. The probability of drawing 2 white marbles without replacement is (7/15) * (6/14) = 21/70. The probability of then drawing 1 red marble is (8/13). So, the overall probability is (21/70) * (8/13).
b. 1 white marble and 2 red marbles: The probability of drawing 1 white marble is (7/15), and then drawing 2 red marbles is (8/14) * (7/13). So, the overall probability is (7/15) * (8/14) * (7/13).
c. 3 white marbles: The probability of drawing 3 white marbles without replacement is (7/15) * (6/14) * (5/13).
d. 3 red marbles: The probability of drawing 3 red marbles without replacement is (8/15) * (7/14) * (6/13).