To find the probability of drawing two marbles of different colors from the bag, we first need to determine the total number of marbles in the bag. The bag contains:
- 6 Red marbles
- 4 Blue marbles
- 7 Green marbles
- 3 Yellow marbles
Adding these together gives us the total number of marbles:
Total Marbles = 6 + 4 + 7 + 3 = 20
Now, let’s look at the total possible outcomes when we draw two marbles. The first marble can be any of the 20 marbles, and after we remove one marble, there will be 19 marbles left to choose from. Thus, the total possible outcomes for drawing two marbles is:
Total Outcomes = 20 * 19 = 380
Next, we can calculate the outcomes for drawing two marbles of the same color. We will calculate this for each color:
- Red Marbles: Drawing two out of 6 red marbles:
Ways = 6C2 = 15 - Blue Marbles: Drawing two out of 4 blue marbles:
Ways = 4C2 = 6 - Green Marbles: Drawing two out of 7 green marbles:
Ways = 7C2 = 21 - Yellow Marbles: Drawing two out of 3 yellow marbles:
Ways = 3C2 = 3
Now, summing these ways gives us the total ways to draw two marbles of the same color:
Same Color Outcomes = 15 + 6 + 21 + 3 = 45
To find the probability of drawing two marbles of different colors, we subtract the same color outcomes from the total outcomes:
Different Color Outcomes = Total Outcomes – Same Color Outcomes
Different Color Outcomes = 380 – 45 = 335
Finally, the probability of drawing two marbles of different colors is calculated as:
Probability (Different Colors) = Different Color Outcomes / Total Outcomes
Probability (Different Colors) = 335 / 380
To express this probability as a decimal, we can perform the division:
Probability (Different Colors) ≈ 0.8842
Thus, the probability of drawing two marbles of different colors from the bag is approximately 0.8842 or 88.42%.