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: an even number on the last roll event b: alternating even number and odd number (with either coming first) event c: more even numbers than odd numbers

Explanation:

Step1: Determine outcomes for Event A

Outcomes with an even number on the last roll are OEO, OEE, EOE, EEE, EEO, OOE. There are 6 such outcomes.

Step2: Calculate probability for Event A

Since there are 8 total outcomes and 6 favorable outcomes for Event A, the probability is $\frac{6}{8}=\frac{3}{4}$.

Step3: Determine outcomes for Event B

Outcomes with alternating even - odd numbers are OEO, EOE, OOE, EOO. There are 4 such outcomes.

Step4: Calculate probability for Event B

The probability is $\frac{4}{8}=\frac{1}{2}$ as there are 8 total outcomes and 4 favorable ones for Event B.

Step5: Determine outcomes for Event C

Outcomes with more even numbers than odd numbers are OEE, EOE, EEE, EEO. There are 4 such outcomes.

Step6: Calculate probability for Event C

The probability is $\frac{4}{8}=\frac{1}{2}$ as there are 8 total outcomes and 4 favorable ones for Event C.

Answer:

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