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 b: an even number on both the first and the last rolls
event c: no odd numbers on the last two rolls

Explanation:

Step1: Identify outcomes for Event A

Outcomes with alternating odd - even are OEO and EOE.

Step2: Calculate probability for Event A

There are 8 total outcomes. Probability = $\frac{2}{8}=\frac{1}{4}$.

Step3: Identify outcomes for Event B

Outcomes with even on first and last are EEE and EEO.

Step4: Calculate probability for Event B

Probability = $\frac{2}{8}=\frac{1}{4}$.

Step5: Identify outcomes for Event C

Outcomes with no odd on last two are OEE, EEE, EEO.

Step6: Calculate probability for Event C

Probability = $\frac{3}{8}$.

Answer:

Event	Outcomes	Probability
Event B	EEE, EEO	$\frac{1}{4}$
Event C	OEE, EEE, EEO	$\frac{3}{8}$