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: more odd numbers than even numbers
event b: an even number on both the first and the last rolls
event c: an even number on the first roll or the second roll (or both)

Explanation:

Step1: Analyze Event A

Count outcomes with more odds. Outcomes are OOE, OEO, EOO, OOO. There are 4 such outcomes. Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{4}{8}=\frac{1}{2}$.

Step2: Analyze Event B

Find outcomes with even - first and even - last. Outcomes are EEO, EEE. There are 2 such outcomes. Probability = $\frac{2}{8}=\frac{1}{4}$.

Step3: Analyze Event C

List outcomes with even on first or second (or both). Outcomes are EEO, EOE, EOO, EEE, OEO, OEE. There are 6 such outcomes. Probability = $\frac{6}{8}=\frac{3}{4}$.

Answer:

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