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

Explanation:

Event A: Alternating odd and even numbers

Step1: Identify valid outcomes

An alternating pattern (either OEO or EOE). From the list: OEO, EOE.

Step2: Calculate probability

Total outcomes \(n = 8\). Favorable outcomes \(m=2\). Probability \(P=\frac{m}{n}\).
$$P=\frac{2}{8}=\frac{1}{4}$$

Event B: More odd numbers than even

Step1: Identify valid outcomes

Count odd numbers in each outcome. Outcomes with 2 or 3 odd numbers: OOE, OOO, EOO.

Step2: Calculate probability

Total outcomes \(n = 8\). Favorable outcomes \(m = 3\). Probability \(P=\frac{m}{n}\).
$$P=\frac{3}{8}$$

Event C: An even number on the second roll

Step1: Identify valid outcomes

Look at the second - character (O or E) in each string. Outcomes: OEE, EEE, EEO, OEO.

Step2: Calculate probability

Total outcomes \(n = 8\). Favorable outcomes \(m = 4\). Probability \(P=\frac{m}{n}\).
$$P=\frac{4}{8}=\frac{1}{2}$$

Answer:

• Event A: Probability \(\frac{1}{4}\)
• Event B: Probability \(\frac{3}{8}\)
• Event C: Probability \(\frac{1}{2}\)