A fair cube has a red face, a blue face, a green face, and a white face. During an experiment, the cube is tossed and the color that it lands on is recorded. The cube lands on red 4 times as often as it lands on blue. The cube lands on blue twice as often as it lands on green, and it lands on green as often as it lands on white. A) Create and complete a probability distribution table of the four colors. B) Draw a bar graph to represent the probability distribution.

To create a probability distribution table for the four colors, we can let the probability of the cube landing on blue be represented by \( p \) (because blue is mentioned as a reference for both red and green). Since the cube lands on red 4 times as often as on blue, the probability of it landing on red is \( 4p \). It lands on blue twice as often as on green, so the probability for green would be \( \frac{p}{2} \), and since it lands on green as often as on white, the probability for white is also \( \frac{p}{2} \).

Now let's write out the probabilities:

Red: \( 4p \) Blue: \( p \) Green: \( \frac{p}{2} \) White: \( \frac{p}{2} \)

Since these are all the sides of the cube and the cube must land on one of these colors, their probabilities must add up to 1.

So we have:

\( 4p + p + \frac{p}{2} + \frac{p}{2} = 1 \)

Combining like terms:

\( 6p = 1 \)

Now, divide both sides by 6 to solve for \( p \):

\( p = \frac{1}{6} \)

Now that we know \( p \), we can find the probability for each color:

Red: \( 4p = 4 \times \frac{1}{6} = \frac{2}{3} \) Blue: \( p = \frac{1}{6} \) Green: \( \frac{p}{2} = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \) White: \( \frac{p}{2} = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \)

So the probability distribution table looks like this:

| Color | Probability | |-------|--------------| | Red | \(\frac{2}{3}\) | | Blue | \(\frac{1}{6}\) | | Green | \(\frac{1}{12}\) | | White | \(\frac{1}{12}\) |

Part B is about drawing a bar graph to represent this probability distribution. To do so,

1. Draw a horizontal line and a vertical line to create an L-shape. The horizontal line will represent the different colors, and the vertical line will represent the probabilities. 2. Mark four evenly spaced points along the horizontal axis for the red, blue, green, and white colors. 3. Along the vertical axis, make marks to represent probabilities, ensuring that you mark at least up to the largest probability (in this case, \(\frac{2}{3}\)). 4. For each color, draw a rectangle (bar) above the color's mark on the horizontal axis. The height of each bar will correlate to the probability of landing on that color; so the red bar will be the tallest, reaching up to the height corresponding to \(\frac{2}{3}\), blue reaching \(\frac{1}{6}\), and green and white each reaching \(\frac{1}{12}\). 5. Make sure each bar is an equal width and there are equal spaces between them. 6. Label each bar with its corresponding color and the vertical axis with appropriate probability values.

Please note that for a precise bar graph, you will need to physically draw it out or use graphing software.