Final answer:
The expected value of the sum of two fair 6-sided dice is 7, but the actual sum can vary between 2 and 12. The statement that the sum could be 5 is true, as is the statement that the average of the sum will be 7 with increasing number of rolls. However, the statement that if the first die lands on 4, the second die will always land on 3 is false. Option 1 is correct.
Step-by-step explanation:
The expected value of the sum of two fair 6-sided dice is indeed 7. This means that, on average, the sum of two fair 6-sided dice will be 7. However, this does not mean that the sum will always be 7. The sum could be any number between 2 and 12, depending on the outcomes of each individual die.
Therefore, the statement 'The sum of two fair 6-sided dice could be 5' is true. It is possible for the sum to be 5 if one die shows a 2 and the other shows a 3, for example.
The statement 'No matter how many times you roll two fair 6-sided dice, the average of the sum of the dice will be exactly 7' is also true. The expected value represents the long-term average, so even if individual rolls have different sums, the average of all rolls will approach 7 as the number of rolls increases.
Finally, the statement 'If the first die lands on 4, the second die will always land on 3' is false. The outcomes of rolling dice are independent events, so the result of the first die does not determine the result of the second die.