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. event a: no odd numbers on the last two rolls event b: alternating odd number and even number (with either coming first) event c: exactly one odd number

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 $n(S) = 8$ (total number of outcomes).

Step2: Analyze Event A

Event A: No odd numbers on the last two rolls. Outcomes are EEE, EEO. So $n(A)=2$. Then $P(A)=\frac{2}{8}=\frac{1}{4}$.

Step3: Analyze Event B

Event B: Alternating odd - number and even - number (with either coming first). Outcomes are EOE, OEO, OEO, EOE. So $n(B)=2$. Then $P(B)=\frac{2}{8}=\frac{1}{4}$.

Step4: Analyze Event C

Event C: Exactly one odd number. Outcomes are EEO, OEE, EOE, OEE. So $n(C)=4$. Then $P(C)=\frac{4}{8}=\frac{1}{2}$.

Answer:

Event	Outcomes Checked	Probability
Event B	EOE, OEO	$\frac{1}{4}$
Event C	EEO, OEE, EOE, OEE	$\frac{1}{2}$