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: exactly one odd number event b: two or more odd numbers event c: no odd numbers on the last two rolls

Explanation:

Step1: Determine total number of outcomes

There are 8 total outcomes as given.

Step2: Analyze Event A

Outcomes with exactly one odd number are EEO, OEE, EOE. So there are 3 such outcomes. Probability of Event A = $\frac{3}{8}$.

Step3: Analyze Event B

Outcomes with two or more odd numbers are OOE, EOO, OOO, OEO. So there are 4 such outcomes. Probability of Event B = $\frac{4}{8}=\frac{1}{2}$.

Step4: Analyze Event C

Outcomes with no odd numbers on the last two rolls are EEO, EEE. So there are 2 such outcomes. Probability of Event C = $\frac{2}{8}=\frac{1}{4}$.

Answer:

Event	Checked Outcomes	Probability
Event B	OOE, EOO, OOO, OEO	$\frac{1}{2}$
Event C	EEO, EEE	$\frac{1}{4}$