Answered

A group of students were asked which club they planned to join.

\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{ Club } & Percent of Students \\
\hline Garden Club & 0.1 \\
\hline Robotics Club & 0.2 \\
\hline Technology Club & 0.5 \\
\hline Zoology Club & 0.2 \\
\hline
\end{tabular}

Compare the probabilities of a randomly selected student joining a club and interpret the likelihood. Choose the statement that is true.

A. The student will be more unlikely to join the Robotics Club than the Garden Club because [tex]$P($[/tex]Robotics[tex]$)\ \textless \ P($[/tex]Garden[tex]$)$[/tex].

B. The student will be equally likely to join the Robotics Club or Technology Club because [tex]$P($[/tex]Robotics[tex]$)= P($[/tex]Technology[tex]$)$[/tex].

C. The student will be more likely to join the Zoology Club than the Robotics Club because [tex]$P($[/tex]Zoology[tex]$)\ \textgreater \ P($[/tex]Robotics[tex]$)$[/tex].

D. The student will be more unlikely to join the Garden Club than the Robotics Club because [tex]$P($[/tex]Garden[tex]$)\ \textless \ P($[/tex]Robotics[tex]$)$[/tex].



Answer :

GinnyAnswer
Let's compare the probabilities given in the problem statement for each club:

- The probability of a student joining the Garden Club ([tex]\(P(\text{Garden})\)[/tex]) is 0.1.
- The probability of a student joining the Robotics Club ([tex]\(P(\text{Robotics})\)[/tex]) is 0.2.
- The probability of a student joining the Technology Club ([tex]\(P(\text{Technology})\)[/tex]) is 0.5.
- The probability of a student joining the Zoology Club ([tex]\(P(\text{Zoology})\)[/tex]) is 0.2.

Now, let's evaluate each statement individually:

1. The student will be more unlikely to join the Robotics Club than the Garden Club because [tex]\(P(\text{Robotics}) < P(\text{Garden})\)[/tex].

- [tex]\(P(\text{Robotics}) = 0.2\)[/tex]
- [tex]\(P(\text{Garden}) = 0.1\)[/tex]
- [tex]\(0.2 \not< 0.1\)[/tex] (This statement is false)

2. The student will be equally likely to join the Robotics Club or Technology Club because [tex]\(P(\text{Robotics}) = P(\text{Technology})\)[/tex].

- [tex]\(P(\text{Robotics}) = 0.2\)[/tex]
- [tex]\(P(\text{Technology}) = 0.5\)[/tex]
- [tex]\(0.2 \neq 0.5\)[/tex] (This statement is false)

3. The student will be more likely to join the Zoology Club than the Robotics Club because [tex]\(P(\text{Zoology}) > P(\text{Robotics})\)[/tex].

- [tex]\(P(\text{Zoology}) = 0.2\)[/tex]
- [tex]\(P(\text{Robotics}) = 0.2\)[/tex]
- [tex]\(0.2 \not> 0.2\)[/tex] (This statement is false)

4. The student will be more unlikely to join the Garden Club than the Robotics Club because [tex]\(P(\text{Garden}) < P(\text{Robotics})\)[/tex].

- [tex]\(P(\text{Garden}) = 0.1\)[/tex]
- [tex]\(P(\text{Robotics}) = 0.2\)[/tex]
- [tex]\(0.1 < 0.2\)[/tex] (This statement is true)

The correct interpretation is:
The student will be more unlikely to join the Garden Club than the Robotics Club because [tex]\(P(\text{Garden}) < P(\text{Robotics})\)[/tex].

So the true statement is:
"The student will be more unlikely to join the Garden Club than the Robotics Club because [tex]\(P(\text{Garden}) < P(\text{Robotics})\)[/tex]."

Therefore, the correct statement index is 4.