Each of the 6 faces of a fair cube is painted red, yellow, or blue. This cube is rolled 500 times. Below shows the number of times each color landed face up.

Red-90 times
yellow- 340 times
blue- 70 times
Based on the results, what is the most likely number of yellow faces on the cube?

red/6 = 90/500 = 9/50

red = 54/50 = 1.08 = appr 1
yellow/6 = 340/500
yellow = 6(34/50) = 4.08 = appr 4
blue/6 = 70/500
blue = 84 = appr 1

it appear that 1 face is red, 1 face is blue, and 4 faces are yellow

To determine the most likely number of yellow faces on the cube, we need to calculate the probability of each scenario and find the highest probability.

We know that a fair cube has 6 faces, so there could be 0, 1, 2, 3, 4, 5, or 6 yellow faces.

To calculate the probabilities, we can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

Where:
- n is the number of trials (500 rolls in this case)
- k is the number of successful outcomes (yellow faces in this case)
- p is the probability of success in a single trial (the probability of rolling a yellow face)

We can calculate the probability for each scenario using the given information:

For k = 0:
P(X=0) = (500 choose 0) * (340/500)^0 * (1-(340/500))^(500-0)

For k = 1:
P(X=1) = (500 choose 1) * (340/500)^1 * (1-(340/500))^(500-1)

And so on, for k = 2, 3, 4, 5, and 6.

To find the most likely number of yellow faces on the cube, we need to compare the probabilities for each scenario and select the one with the highest probability.

To determine the most likely number of yellow faces on the cube, we need to find the probability of each scenario and then determine which scenario has the highest probability based on the given results.

The total number of rolls is 500, and the result of each color is as follows:
- Red: 90
- Yellow: 340
- Blue: 70

To find the probability of each scenario, we divide the number of times a color appears by the total number of rolls:

Probability of Red = 90/500 = 0.18
Probability of Yellow = 340/500 = 0.68
Probability of Blue = 70/500 = 0.14

Therefore, based on the given results, the most likely number of yellow faces on the cube is 4 (out of 6 faces), as it has the highest probability of occurring.