11. Two fair dice are rolled. Find the probability that both dice have the same number.

When two fair dice are rolled, there are a total of 36 possible outcomes (6 sides on the first die multiplied by 6 sides on the second die). The successful outcomes for both dice showing the same number are (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6) — a total of 6 outcomes. Therefore, the probability that both dice have the same number is calculated by dividing the number of successful outcomes by the total outcomes: P(same number) = 6/36 = 1/6. Rolling two dice isn't just about numbers; it's like throwing a mini-party! Each die has its own personality and gets to contribute to the overall vibe. Who knew that probability could be a group of buddies? When you find both dice having the same number, it's like they sync up for a dance—whether it's matching twos, threes, or any other number, you're always in for a fun surprise when you roll those dice! So, what can you do with this knowledge? You could host a game night where you roll two dice to determine fun challenges or prizes. Teach your friends the art of calculating probabilities while you play! Or use these skills in board games and dice games like Craps or Liar’s Dice for some thrilling competition. Understanding probability not only spices up your games but also sharpens your skills in decision-making. Let's roll!