This would be the 1 - (probability of both yellow + both red + both green)
Probability is thing of interest / total. AND means multiply.
There are 15 total marbles. Without replacement means the second draw will be out of 14 marbles, and each time it will have one less of whatever color was drawn the first time.
Probability of both yellow without replacement (yellow and yellow) is 6/15 * 5/14 = 3/3 * 1/7 = 3/21
Probability of both red without replacement (red and red) is 5/15 * 4/14 = 1/3 * 2/7 = 2/21
Probability of both green without replacement (green and green) is 4/15 * 3/14 = 2/5 * 1/7 = 2/35
1 - (3/21 + 2/21 + 2/35) = 1 - (5/21 + 2/35) = 1 - (25/105 + 6/105) = 1 - 31/105 = 105/105 - 31/105 = 74/105
