Answered

IDNLearn.com offers a comprehensive platform for finding and sharing knowledge. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.

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.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline
& \multicolumn{8}{|c|}{Outcomes} & \multirow{2}{*}{Probability} \\
\hline
& 000 & EOO & EOE & EEO & OOE & OEO & OEE & EEE & \\
\hline
\begin{tabular}{l}
Event A: An even number on both the \\
first and the last rolls
\end{tabular}
& [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & \\
\hline
\begin{tabular}{l}
Event B: An odd number on each of \\
the last two rolls
\end{tabular}
& [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & \\
\hline
\begin{tabular}{l}
Event C: An even number on the last \\
roll
\end{tabular}
& [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & [tex]$\square$[/tex] & \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
Sure, let's work through the problem step by step. We will determine the outcomes for each event and their respective probabilities.

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

Conditions:
- First roll: Even ('E')
- Last roll: Even ('E')

Possible Outcomes:
- EOE
- EEE

Probability Calculation:
There are 8 possible outcomes in total. The outcomes satisfying Event A are EOE and EEE.

- Number of favorable outcomes = 2
- Total number of possible outcomes = 8

Probability of Event A = (Number of favorable outcomes) / (Total number of possible outcomes)
[tex]\[ P(A) = \frac{2}{8} = 0.25 \][/tex]

### Event B: An odd number on each of the last two rolls

Conditions:
- Second roll: Odd ('O')
- Last roll: Odd ('O')

Possible Outcomes:
- OOO
- EOO

Probability Calculation:
There are 8 possible outcomes in total. The outcomes satisfying Event B are OOO and EOO.

- Number of favorable outcomes = 2
- Total number of possible outcomes = 8

Probability of Event B = (Number of favorable outcomes) / (Total number of possible outcomes)
[tex]\[ P(B) = \frac{2}{8} = 0.25 \][/tex]

### Event C: An even number on the last roll

Condition:
- Last roll: Even ('E')

Possible Outcomes:
- OOE
- OEE
- EOE
- EEE

Probability Calculation:
There are 8 possible outcomes in total. The outcomes satisfying Event C are OOE, OEE, EOE, and EEE.

- Number of favorable outcomes = 4
- Total number of possible outcomes = 8

Probability of Event C = (Number of favorable outcomes) / (Total number of possible outcomes)
[tex]\[ P(C) = \frac{4}{8} = 0.5 \][/tex]

### Summary of Results

| Event | Favorable Outcomes | Probability |
|----------------------------|---------------------------------|-------------|
| Event A: An even number on both the first and the last rolls | EOE, EEE | 0.25 |
| Event B: An odd number on each of the last two rolls | OOO, EOO | 0.25 |
| Event C: An even number on the last roll | OOE, OEE, EOE, EEE | 0.5 |

Thus, we have correctly identified the favorable outcomes and calculated the probabilities for each event.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.