Suppose a box of marbles contains equal numbers of red marbles and yellow marbles but twice as many green marbles as red marbles. Draw one marble from the box and observe its color. Assign probabilities to the elements in the sample space. (Give your answers as fractions.)
Red Incorrect: Your answer is incorrect. .
Green Incorrect: Your answer is incorrect. .
Yellow
I got 1/3; 2/3; and 1/3 but answers were wrong
To assign probabilities to the elements in the sample space, you need to consider the given information. Let's break it down step-by-step:
1. The box contains equal numbers of red marbles and yellow marbles.
2. There are twice as many green marbles as red marbles.
Based on these two pieces of information, we can determine the following probabilities:
1. Probability of drawing a red marble:
Since the box contains an equal number of red and yellow marbles, the probability of drawing a red marble is the number of red marbles divided by the total number of marbles in the box. Let's represent the number of red marbles as R. The total number of marbles in the box is R (for red marbles) + R (for yellow marbles) + 2R (for green marbles) = 4R. Therefore, the probability of drawing a red marble is R/4R = 1/4.
2. Probability of drawing a green marble:
Since there are twice as many green marbles as red marbles, the number of green marbles is 2R. Therefore, the probability of drawing a green marble is 2R/4R = 1/2.
3. Probability of drawing a yellow marble:
Similarly, the number of yellow marbles is also R (equal to the number of red marbles). Therefore, the probability of drawing a yellow marble is R/4R = 1/4.
Hence, the correct probabilities for the sample space elements are:
- Probability of drawing a red marble: 1/4
- Probability of drawing a green marble: 1/2
- Probability of drawing a yellow marble: 1/4
To assign probabilities to the elements in the sample space in this scenario, we first need to determine the total number of marbles in the box.
Let's assume the number of red marbles is represented by "x". Since the box contains an equal number of red marbles and yellow marbles, there will also be "x" yellow marbles.
According to the given information, there are twice as many green marbles as red marbles. So the number of green marbles will be 2 times "x", which is 2x.
The total number of marbles in the box is equal to the sum of the number of red, yellow, and green marbles:
Total = red + yellow + green
Total = x + x + 2x
Total = 4x
Now, we can assign probabilities to each element in the sample space by dividing the number of marbles of that color by the total number of marbles:
Probability of drawing a red marble: (number of red marbles) / (total number of marbles) = x / 4x = 1/4
Probability of drawing a green marble: (number of green marbles) / (total number of marbles) = 2x / 4x = 1/2
Probability of drawing a yellow marble: (number of yellow marbles) / (total number of marbles) = x / 4x = 1/4
Therefore, the correct probabilities for the elements in the sample space are:
Red: 1/4
Green: 1/2
Yellow: 1/4