Final answer:
The probability of getting at least one 7 when rolling a pair of dice 3 times is approximately 42.13%.
Step-by-step explanation:
To calculate the probability of getting at least one 7 when rolling a pair of dice 3 times, we can use the concept of complementary events. Let's find the probability of not rolling a 7 in a single roll. The possible outcomes for rolling two dice are: {(1,1), (1,2), (1,3), ..., (6,6)}. There are 36 possible outcomes and only 6 outcomes that result in a sum of 7. So the probability of not rolling a 7 in a single roll is 30/36.
To find the probability of not rolling a 7 in three rolls, we multiply the probabilities of not rolling a 7 in each roll. So the probability of not rolling a 7 in three rolls is (30/36) * (30/36) * (30/36) = 0.5787.
The probability of rolling at least one 7 in three rolls is the complement of not rolling a 7 in three rolls. So the probability of rolling at least one 7 is 1 - 0.5787 = 0.4213, or approximately 42.13%.