a number cube is rolled three times. an outcome is represented by a string of the sort oee (meaning an odd…

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 both the first and the last rolls event b: two or more odd numbers event c: an odd number on each of the first two rolls

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 both the first and the last rolls event b: two or more odd numbers event c: an odd number on each of the first two rolls

Answer

Explanation:

Step1: Determine total number of outcomes

There are 8 total outcomes as given in the table. Each outcome has a probability of $\frac{1}{8}$.

Step2: Analyze Event A

Event A is an even number on both the first and the last rolls. The outcomes that satisfy this are EEE and EEO. So there are 2 favorable outcomes. Probability of Event A = $\frac{2}{8}=\frac{1}{4}$.

Step3: Analyze Event B

Event B is two or more odd - numbers. The outcomes that satisfy this are OOO, OOE, OEO, EOO. So there are 4 favorable outcomes. Probability of Event B = $\frac{4}{8}=\frac{1}{2}$.

Step4: Analyze Event C

Event C is an odd number on each of the first two rolls. The outcomes that satisfy this are OOE, OOO. So there are 2 favorable outcomes. Probability of Event C = $\frac{2}{8}=\frac{1}{4}$.

Answer:

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