I'm currently working on a probability problem and could use some assistance. The problem involves three six-sided dice: one blue die and two red dice. I'm trying to determine the probability of exactly one of the red dice showing the same number of dots as the blue die.
Here's my attempt at solving it:
To find the probability, I started by considering the possible outcomes and favorable outcomes:
Possible outcomes: Each die has six possible outcomes since they are six-sided dice.
Favorable outcomes: To have exactly one of the red dice match the blue die, I need to choose one of the two red dice and match its dots with the blue die. Each red die has six possible outcomes, considering the six sides. So, there are a total of $2 \cdot 6 = 12$ favorable outcomes.
Using the formula for probability (favorable outcomes divided by possible outcomes), I attempted to calculate the probability as follows:
Probability = favorable outcomes / possible outcomes = 12 / (2 * 6) = 12 / 12 = 1
Therefore, my initial calculation suggests that the probability is 1 or 100%. This would mean it's certain that exactly one of the red dice will match the number of dots on the blue die.
Could someone please verify my approach and calculations? If I made any mistakes or if there's a more accurate method to solve this problem, I would greatly appreciate your guidance.
Thank you in advance for your help!