To solve this problem, let's go back to probability first principles. We need to know how many possible selections there are, and this will be the denominator of the fraction. We also need to know how many ways a success can happen, and this will be the numerator.
These are selections without replacement, since the marbles are being set aside. Order doesn't matter, so these are combinations.
The number of ways that 7 distinct marbles can be selected from 9 total marbles is 9C7, which is 36. This will be the denominator.
The numerator is a little more tricky. We need to individuate the selections based on how many of each color we have. We have 2 red marbles, and for a success, both need to be selected. We have 7 white marbles. Because 2 of our selected marbles are red, then the remaining 5 selected marbles must be white. So, our selection of white marbles is 5 out of 7. These make the combinations 2C2 and 7C5, respectively. Since both independently occur together, they are multiplied together. 2C2 = 1, and 7C5 = 21, so the total number of ways a success can happen is 1 • 21 = 21. This is the numerator.
The probability, then, is 21/36, or 7/12.
