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 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: Calculate the probability for Event A

Event A is an even number on the second roll.
The total number of outcomes \(n = 8\).
The number of outcomes with an even number on the second roll: OEE, EEO, OOE, EEE, OEO, EOE. So \(m_A=6\).
The probability \(P(A)=\frac{m_A}{n}=\frac{6}{8}=\frac{3}{4}\).

Step2: Calculate the probability for Event B

Event B is alternating even and odd numbers.
The outcomes that satisfy this are EOO, OEO. So \(m_B = 2\).
The probability \(P(B)=\frac{m_B}{n}=\frac{2}{8}=\frac{1}{4}\).

Step3: Calculate the probability for Event C

Event C is two or more even numbers.
The outcomes that satisfy this are OEE, EEO, OOE, EEE, EOE. So \(m_C=5\).
The probability \(P(C)=\frac{m_C}{n}=\frac{5}{8}\).

Answer:

Event A: \(\frac{3}{4}\)
Event B: \(\frac{1}{4}\)
Event C: \(\frac{5}{8}\)