Fairness of Loaded Dice?

📌 CONCEPT: The fairness of a die can be determined by comparing the probability of getting a specific number on the die with the expected probability in a standard die, which is 1/6 for each number.

📐 RULE / FORMULA: For a standard die, the probability of getting a specific number is 1/6. For the loaded dice, the probabilities are given as 0.4 and 0.5 for two different numbers.

💡 WORKED EXAMPLE: Comparing the loaded dice with the standard die, we can see that one die is even more biased (0.4) than the standard die, while the other die is slightly less biased (0.5), but not as fair as a standard die. This difference in biases indicates that the two loaded dice are not fair.

⚠️ COMMON MISTAKE: Students might mistakenly assume that a die with a higher probability for a specific number is fairer than a standard die, when in fact, the fairness is determined by the comparison with the standard die's probabilities.