The probability of 2 green outcomes and 2 orange outcomes when you roll the number cube 4 times is 0.116.
Assuming that it is a fair number cube, the probability of getting green is given by the quotient between the outcomes that give the color green and the total number of outcomes.
We know that there are 5 green sides (so 5 outcomes give the color green) and the dice has 6 sides (so there is a total of 6 outcomes). Then the probability of rolling green is:
P = 5/6.
The probability of rolling orange is computed in the same way, 1 outcome gives the color orange and there are 6 outcomes in total, so the probability of getting orange is:
Q = 1/6.
Now, let's assume that when we roll four times we get:
green - green - orange - orange.
The probability of that is given by the product of the individual probabilities, it is:
p = P*P*Q*Q = (5/6)*(5/6)*(1/6)*(1/6).
Now, we also need to take in account all the possible permutations, these are:
So there are 6 permutations, to get the total probability of rolling 2 green outcomes and 2 orange outcomes, we need to multiply this number by the probability we got above.
Probability = 6p = 6* (5/6)*(5/6)*(1/6)*(1/6) = 0.116
If you want to learn more about probability, you can read:
https://brainly.com/question/251701
