Question

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. 000 or EEE
B. OEO or OOE or EOO
C. OEE or EEO or EOE
D. 000 or EEE or OEO or OOE or EOO
E. OEE or EEO or EOE or OOO or EEE

Answer 1

The complement of the event where exactly two even rolls are recorded includes all other outcomes: OOO, EEE, OEO, OOE, or EOO.

Step-by-step explanation:

The complement of the event in which exactly two even rolls are recorded is the set of all other possible outcomes when a number cube is rolled three times. Since the outcomes with exactly two even rolls (like OEE, EEO, or EOE) are what we want to avoid, the complement would include all other combinations (OOO, EEE, OEO, OOE, EOO, and EEO) except the ones with exactly two evens.

Therefore, the correct answer is D. OOO or EEE or OEO or OOE or EOO, as these are the combinations where there are not exactly two even numbers (E represents an even roll and O represents an odd roll).