Final answer:
The probability that two marbles drawn will be the same color is calculated by summing the individual probabilities of drawing two marbles of each color (blue, green, or red) without replacement, which totals approximately 31.11%.
Step-by-step explanation:
To find the probability that two marbles drawn from a bag are the same color, we can calculate the likelihood of drawing two blue, two green, or two red marbles and then sum these probabilities.
For two blue marbles, the probability is (5/10) * (4/9) = 20/90 because after drawing one blue marble, there are only 4 blue marbles left out of 9 total marbles.
For two green marbles, the probability is (3/10) * (2/9) = 6/90 because there are 2 green marbles left after one is drawn.
For two red marbles, the probability is (2/10) * (1/9) = 2/90, as only 1 red marble remains after the first is drawn.
Adding these probabilities together gives us (20+6+2)/90 = 28/90 or about 31.11%. So, the probability that the marbles will be the same color is 31.11%.
Notice that without replacement, the total number of marbles and the number of a specific color reduce after the first draw, which affects the second draw's probability.