Answer: The probability is 1/9.
Step-by-step explanation:
First, let's define the possible outcomes of each dice:
Red: Forward (4 times), Backward (2 times)
Green : {1, 1, 2, 2, 3, 4}
We want to find the probability of moving backward 2 spaces.
Then we need to find the probability of rolling a "backward" in the red dice, and a 2 in the green dice.
First, the probability of rolling a backward in the red dice is equal to the quotient between the number of outcomes that are "backward", and the total number of outcomes in the dice (there are 2 backwards and 6 outcomes in total), this is:
p1 = 2/6 = 1/3.
And the probability of rolling a 2 in the green dice is equal to the quotient between the number of outcomes with a 2, and the total number of outcomes. (The 2 appears two times, and there are 6 possible outcomes):
p2 = 2/6 = 1/3.
Now, the probability of both events happening at the same time is equal to the product of the individual probabilities, then the probability of moving backwards 2 spaces is:
P = p1*p2 = (1/3)*(1/3) = 1/9.
