Hi BrentGreenlightTestPrep
Question state simultaneously and at random, therfore wondering why is denominator not 6 for both instances?

VERITAS PREP OFFICIAL SOLUTION:

Solution: 8/15. There are two paths to one of each color: Red, then White; or White, then Red. So you’ll need to calculate the probability of each sequence and add them together.

Red, then White: There’s a 4/6 probability of drawing Red first, and then there will be 2 White left to draw from the remaining 5 marbles. So that’s a probability of 2/3 * 2/5 for a total of 4/15.

White, then Red: there’s a 2/6 probability of drawing White first, at which point there would be 4 Red left to draw from the remaining 5 marbles. That’s a probability of 1/3 * 4/5 = 4/15. Add together the two probabilities to get the total probability of one of each, and you get a total of 8/15.

Solution:

The number of ways he can choose 2 marbles is 6C2 = (6 x 5)/2 = 15. The number of ways he can choose 1 marble of each color is 4C1 x 2C1 = 4 x 2 = 8. Therefore, the probability of picking one marble of each color is 8/15.

Alternate Solution:

Lionel can choose either R-W or W-R. The probability of R-W is 4/6 x 2/5 = 8/30 = 4/15, and the probability of W-R is 2/6 x 4/5 = 8/30 = 4/15. Thus, the probability of picking one marble of each color is 4/15 + 4/15 = 8/15.

Answer: B

Hi Carcass, thanks for your reply.
Presumed I just need to ignore the word "simultaneously" and calculate it as normal then...