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 last two rolls
event b: exactly one odd number
event c: two or more even numbers

Explanation:

Step1: Determine total number of outcomes

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

Step2: Analyze Event A

Event A: An odd number on each of the last two rolls.
For a string of the form \(xOO\) (where \(x\) can be odd or even).
The outcomes are \(OOO\) and \(EOO\).
The number of favorable outcomes \(m_A=2\).
The probability \(P(A)=\frac{m_A}{n}=\frac{2}{8}=\frac{1}{4}\)

Step3: Analyze Event B

Event B: Exactly one odd number.
The outcomes are \(EOE\), \(OEE\), \(EEO\).
The number of favorable outcomes \(m_B = 3\).
The probability \(P(B)=\frac{m_B}{n}=\frac{3}{8}\)

Step4: Analyze Event C

Event C: Two or more even numbers.
The outcomes are \(EOE\), \(EEO\), \(OEE\), \(EEE\).
The number of favorable outcomes \(m_C=4\).
The probability \(P(C)=\frac{m_C}{n}=\frac{4}{8}=\frac{1}{2}\)

Answer:

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