To determine the probability of drawing two marbles of the same color from the bag, we first need to calculate the total number of marbles in the bag.
There are:
- 6 red marbles
- 4 blue marbles
- 7 green marbles
- 3 yellow marbles
This gives us a total of:
Total Marbles = 6 + 4 + 7 + 3 = 20
Now, when we draw the first marble, it can be any of the colors. After drawing the first marble, we do not replace it, which affects the total number of marbles for the second draw.
We will calculate the probability of drawing two marbles of the same color for each color:
- Red Marbles:
Probability of drawing a red marble first:6/20
Probability of drawing a second red marble:5/19 - Blue Marbles:
Probability of drawing a blue marble first:4/20
Probability of drawing a second blue marble:3/19 - Green Marbles:
Probability of drawing a green marble first:7/20
Probability of drawing a second green marble:6/19 - Yellow Marbles:
Probability of drawing a yellow marble first:3/20
Probability of drawing a second yellow marble:2/19
The total probability of drawing two marbles of the same color is the sum of the probabilities of each color.
Calculating these probabilities:
- For red marbles:
(6/20) * (5/19) = 30/380 - For blue marbles:
(4/20) * (3/19) = 12/380 - For green marbles:
(7/20) * (6/19) = 42/380 - For yellow marbles:
(3/20) * (2/19) = 6/380
Now, adding these probabilities together:
Total Probability = 30/380 + 12/380 + 42/380 + 6/380 = 90/380 = 9/38
Therefore, the probability of drawing two marbles of the same color from the bag is 9/38.