A number cube, labeled \( 1-6 \), is rolled three times. The results of the rolls are recorded as odd or even. For example, rolling a 3, then a 4 , and then a 4 again would be recorded as OEE. Rolling a 2, then a 5 , and then a 6 would be recorded as EOE. What is the complement of the event in which exactly two even rolls are recorded? A. OOO or EEE B. OEO or OOE or EOO C. OEE or EEO or EOE D. OOO or EEE or OEO or OOB or EOO E. OEE or EEO or EOE or OOO or EEE

To find the complement of the event where exactly two even rolls are recorded, we first need to understand what the event encompasses. The event of rolling exactly two even numbers (even rolls) can be denoted as combinations such as OEE, EEO, and EOE. The complement involves all other outcomes where either no even rolls (OOO) or all rolls are even (EEE), or only one even roll is recorded. Therefore, the correct answer includes those combinations. The outcomes for rolling a number cube three times amount to a total of \(2^3 = 8\) outcomes categorizing them as odd (O) and even (E). The event of having exactly two even rolls is just one part of the total possibilities. So, the complement consists of the scenarios where there are no even rolls (OOO), one even roll (OEO, OOE, or EOO), or three even rolls (EEE). In conclusion, the answer describing this complement scenario is D.