Question

i have two cubes such that, on each cube, three faces are painted red and three faces are painted white. if i roll each of the cubes once, what is the probability that they will land such that there is one red face and one white face up?

Answer 1

The probability of rolling two cubes such that one shows a red face and the other a white face is 50% or 1/2, because each face color has an independent probability of 1/2 and there are two favorable outcomes.

Step-by-step explanation:

The question is about calculating the probability that when two cubes are rolled, one will show a red face and the other a white face.

To begin with, for each cube the probability of landing on a red face (let's denote it as R) is 3/6 or 1/2, since there are 3 red faces out of 6. Similarly, the probability of landing on a white face (denoted W) is also 3/6 or 1/2.

When rolling two cubes, there are four possible combinations for the colors facing up: (R, R), (R, W), (W, R), and (W, W). Out of these, the combinations (R, W) and (W, R) are favorable for the scenario we're interested in.

The probability for each cube independently is 1/2 to land on a red or a white face. Therefore, the combined probability of having one cube show red and the other show white (either (R, W) or (W, R)) is (1/2 × 1/2) + (1/2 × 1/2), which simplifies to 1/4 + 1/4 = 1/2 or 50%.

So, the probability that one cube will land on a red face and the other on a white face is 50% or 1/2. This is a simple example of a combinatorial probability problem where you are dealing with multiple independent events.