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