Question

a number cube is rolled three times. an outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). the 8 outcomes are listed in the table below. note that each outcome has the same probability. for each of the three events in the table, check the outcome(s) that are contained in the event. then, in the last column, enter the probability of the event.

	outcomes	probability
event a: alternating even number and odd number (with either coming first)
event b: more even numbers than odd numbers
event c: an even number on the first roll or the second roll (or both)

Explanation:

Step1: Recall probability formula

The probability of an event $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in the event $E$ and $n(S)$ is the number of elements in the sample - space. Here, $n(S) = 8$.

Step2: Determine outcomes for Event A

For Event A (alternating even and odd number), the outcomes are OEO and EOE. So $n(A)=2$. Then $P(A)=\frac{2}{8}=\frac{1}{4}$.

Step3: Determine outcomes for Event B

For Event B (more even numbers than odd numbers), the outcomes are EEO, EOO, OEE, EEE. So $n(B) = 4$. Then $P(B)=\frac{4}{8}=\frac{1}{2}$.

Step4: Determine outcomes for Event C

For Event C (an even number on the first roll or the second roll or both), the outcomes are EOE, QOE, EEO, EOO, OEE, EEE. So $n(C)=6$. Then $P(C)=\frac{6}{8}=\frac{3}{4}$.

Answer:

Event	Outcomes	Probability
Event B	EEO, EOO, OEE, EEE	$\frac{1}{2}$
Event C	EOE, QOE, EEO, EOO, OEE, EEE	$\frac{3}{4}$