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

Explanation:

Event A: An odd number on each of the first two rolls

Step1: Identify relevant outcomes

Outcomes where first two rolls are odd: OOO, OOE

Step2: Calculate probability

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

Event B: An even number on both the first and the last rolls

Step1: Identify relevant outcomes

Outcomes where first and last are even: EOO, EEO

Step2: Calculate probability

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

Event C: Two or more odd numbers

Step1: Identify relevant outcomes

Outcomes with two or more odds: OOE, OOO, OEO, EOO

Step2: Calculate probability

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

Answer:

• Event A: Check OOO, OOE. Probability \(\frac{1}{4}\)
• Event B: Check EOO, EEO. Probability \(\frac{1}{4}\)
• Event C: Check OOE, OOO, OEO, EOO. Probability \(\frac{1}{2}\)