a number cube, labeled 1 - 6, is rolled three times. the results of the rolls are recorded as odd or even…

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 ooe or eoo e. oee or eeo or eoe or ooo or eee

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 ooe or eoo e. oee or eeo or eoe or ooo or eee

Answer

Explanation:

Step1: Understand the sample - space

The possible outcomes of each roll are odd (O) or even (E). When rolling a number cube 3 times, the total number of possible sequences is (2\times2\times2 = 8) (by the multiplication principle).

Step2: List the cases of exactly two even rolls

The cases of exactly two even rolls are OEE, EEO, EOE.

Step3: Find the complement

The complement of an event A is all the outcomes in the sample - space that are not in A. The sample - space of all possible sequences of 3 rolls is {OOO, OOE, OEO, EOO, OEE, EEO, EOE, EEE}. Removing the cases of exactly two even rolls (OEE, EEO, EOE) from the sample - space, we get {OOO, OOE, OEO, EOO, EEE}.

Answer:

D. OOO or EEE or OEO or OOE or EOO