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
ooo
eeo
oee
eoo
oeo
ooe
eoe

event a: exactly one odd number
event b: an even number on the first roll
event c: more odd numbers than even numbers

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: Analyze Event A

Event A: Exactly one odd number. The outcomes with exactly one odd number are EEO, OEE, and EOE. So $n(A)=3$. Then $P(A)=\frac{3}{8}$.

Step3: Analyze Event B

Event B: An even number on the first roll. The outcomes with an even number on the first roll are EEE, EEO, EOO, and EOE. So $n(B)=4$. Then $P(B)=\frac{4}{8}=\frac{1}{2}$.

Step4: Analyze Event C

Event C: More odd numbers than even numbers. The outcomes with more odd numbers than even numbers are OOO, OOE, OEO, and EOO. So $n(C)=4$. Then $P(C)=\frac{4}{8}=\frac{1}{2}$.

Event	Outcomes	Probability
Event B	EEE, EEO, EOO, EOE	$\frac{1}{2}$
Event C	OOO, OOE, OEO, EOO	$\frac{1}{2}$

Answer:

Event	Checked Outcomes	Probability
Event B	EEE, EEO, EOO, EOE	$\frac{1}{2}$
Event C	OOO, OOE, OEO, EOO	$\frac{1}{2}$