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.)

Question

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

Answer 1

1/4 1/2 1/4

I got these answers correct.

Answer 2

1/2 MARBLES

Answer 3

To assign probabilities to the elements in the sample space, we need to consider the ratio of each color of marbles in the box.

Given:
- Equal numbers of red marbles and yellow marbles
- Twice as many green marbles as red marbles

Let's assign probabilities to each color:

1. Red Marbles:
Since the box contains an equal number of red and yellow marbles, the probability of drawing a red marble is equal to the ratio of red marbles to the total number of marbles. Let's say there are "x" red marbles.

Probability of drawing a red marble = number of red marbles / total number of marbles
= x / (x + x + 2x)
= x / (4x)
= 1 / 4

So, the probability of drawing a red marble is 1/4.

2. Green Marbles:
The box contains twice as many green marbles as red marbles. Let's say there are "2x" green marbles.

Probability of drawing a green marble = number of green marbles / total number of marbles
= 2x / (x + x + 2x)
= 2x / (4x)
= 1 / 2

So, the probability of drawing a green marble is 1/2.

3. Yellow Marbles:
Since the box contains an equal number of red and yellow marbles, the probability of drawing a yellow marble is equal to the ratio of yellow marbles to the total number of marbles. Let's say there are "y" yellow marbles.

Probability of drawing a yellow marble = number of yellow marbles / total number of marbles
= y / (x + x + 2x)
= y / (4x)
= y / (4 * 1)

So, the probability of drawing a yellow marble is y/4.

Note: The specific value of y is not given, so we cannot determine the exact probability for yellow marble without additional information.

Answer 4

To solve this problem, we need to understand the given information. Let's break it down step by step:

1. The box contains equal numbers of red marbles and yellow marbles: This means that there are the same number of red and yellow marbles.

2. The box also contains twice as many green marbles as red marbles: This means that the number of green marbles is twice the number of red marbles.

Now, let's assign probabilities to the elements in the sample space:

1. Red marbles: Since the box contains an equal number of red and yellow marbles, the probability of drawing a red marble can be calculated as the number of red marbles divided by the total number of marbles. Let's say there are 'x' red marbles. So, the probability of drawing a red marble is x/(x + x + 2x) = x/4x = 1/4.

2. Green marbles: As mentioned, there are twice as many green marbles as red marbles. So, the number of green marbles is 2x. Therefore, the probability of drawing a green marble would be 2x/(x + x + 2x) = 2x/4x = 1/2.

3. Yellow marbles: Since we know that the box contains an equal number of red and yellow marbles, the probability of drawing a yellow marble would be the same as the probability of drawing a red marble, which is 1/4.

Therefore, the correct probabilities for the elements in the sample space are:

Red: 1/4
Green: 1/2
Yellow: 1/4