1/4 1/2 1/4
I got these answers correct.
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
I got these answers correct.
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.
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