Question

You are playing a board game with your little sister. Moves are determined by rolling 2 six-sided dice. The red die tells you the direction of your move, and has 4 faces
that say "forward and 2 faces that say backward." The green die tells you how far to move, and has 1. 1. 2.2.3, and 4 on the faces. On your turn, what is the
probability that you move backward 2 spaces

Answer 1

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.