A bag contains 3 red, 5 yellow, 2 green and 6 blue marbles. If one marble is chosen at random, replaced, and then a second marble is chosen at random, find the probability of obtaining 2 marbles of different colors.
1/3
To find the probability of obtaining 2 marbles of different colors, we need to calculate the probability of choosing a marble of one color on the first draw and a marble of a different color on the second draw.
First, we need to find the total number of marbles in the bag: 3 red + 5 yellow + 2 green + 6 blue = 16 marbles.
Now, let's calculate the probability of choosing a marble of one color on the first draw. There are 16 marbles in total, so the probability of choosing any specific color is:
- Red: 3/16
- Yellow: 5/16
- Green: 2/16
- Blue: 6/16
Next, we need to calculate the probability of choosing a marble of a different color on the second draw. After replacing the first marble, there are still 16 marbles in the bag. Since we want to choose a different color on the second draw, we need to subtract the probability of choosing the same color as the first draw. The probability of choosing a specific color is the same as before:
- Red: 3/16
- Yellow: 5/16
- Green: 2/16
- Blue: 6/16
Now, let's calculate the probability of choosing two marbles of different colors. Since the first draw and second draw are independent events, we can multiply their probabilities:
Probability of different color on the first draw = (3/16) * (13/16) = 39/256
Probability of different color on the second draw = (13/16) * (3/16) = 39/256
Finally, we need to add these two probabilities together to find the probability of obtaining 2 marbles of different colors:
Probability of different color on both draws = (39/256) + (39/256) = 78/256 = 39/128
Therefore, the probability of obtaining 2 marbles of different colors is 39/128.