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? \\(\bigcirc\\) a. ooo or eee \\(\bigcirc\\) b. oeo or ooe or eoo \\(\bigcirc\\) c. oee or eeo or eoe \\(\bigcirc\\) d. ooo or eee or oeo or ooe or eoo \\(\bigcirc\\) e. oee or eeo or eoe or ooo or eee

Explanation:

Step1: Define the event and its complement

The event in question is "exactly two even rolls" in three rolls. The complement of an event is all the outcomes that are not in the event. So we need to find all outcomes where the number of even rolls is not exactly two (i.e., 0, 1, or 3 even rolls).

Step2: Analyze the number of even rolls for each case

• 0 even rolls (all odd): This is the outcome OOO.
• 1 even roll (two odd): The possible arrangements are OEO, OOE, EOO (these are the permutations of one E and two Os).
• 3 even rolls (all even): This is the outcome EEE.

Now, the event "exactly two even rolls" has outcomes with two Es and one O, which are OEE, EEO, EOE. So the complement should be all outcomes that are not OEE, EEO, EOE. From the above analysis, the complement outcomes are OOO (0 even), EEE (3 even), and OEO, OOE, EOO (1 even).

Answer:

D. OOO or EEE or OEO or OOE or EOO