Final answer:
The probability of rolling a sum of 5 on at least one of two rolls of a pair of number cubes is 1/11.
Step-by-step explanation:
To calculate the probability of rolling a sum of 5 on at least one of two rolls of a pair of number cubes, we can use the concept of complementary probability. The probability of an event occurring is equal to 1 minus the probability of the event not occurring. In this case, the event is rolling a sum of 5 on at least one of the two rolls.
The easiest way to approach this problem is to calculate the probability of not rolling a sum of 5 on any of the two rolls. Let's break it down:
- There are 11 possible outcomes when rolling two number cubes: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5).
- Out of these 11 outcomes, there is only one outcome that gives a sum of 5: (2,3).
- Hence, the probability of not rolling a sum of 5 on any of the two rolls is 10/11 (as 10 outcomes do not give a sum of 5).
To find the probability of rolling a sum of 5 on at least one of the two rolls, we subtract the probability of not rolling a sum of 5 from 1:
P(rolling a sum of 5 on at least one of the two rolls) = 1 - P(not rolling a sum of 5) = 1 - 10/11 = 1/11.