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 oee eoo ooo eeo ooe eee oeo eoe probability event a: an even number on the second roll event b: alternating even number and odd number (with either coming first) event c: two or more even numbers

Explanation:

Step1: Count total outcomes

There are \(n = 8\) total outcomes.

Step2: Calculate probability for Event A

For Event A (even on second roll), the favorable outcomes are OEE, EEO, EEE, EOE. So \(m_A=4\). Probability \(P(A)=\frac{m_A}{n}=\frac{4}{8}=\frac{1}{2}\).

Step3: Calculate probability for Event B

For Event B (alternating even and odd), the favorable outcomes are EOO, OEO. So \(m_B = 2\). Probability \(P(B)=\frac{m_B}{n}=\frac{2}{8}=\frac{1}{4}\).

Step4: Calculate probability for Event C

For Event C (two or more evens), the favorable outcomes are OEE, EEO, OOE, EEE, EOE. So \(m_C=5\). Probability \(P(C)=\frac{m_C}{n}=\frac{5}{8}\).

Answer:

Event A: Probability \(\frac{1}{2}\)
Event B: Probability \(\frac{1}{4}\)
Event C: Probability \(\frac{5}{8}\)