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The table below shows the students in an Algebra 1 class.

What is the probability that a randomly chosen student will be a girl given that the student does not own a graphing calculator?

(Note: If your fraction will reduce, you need to reduce it.)

\begin{tabular}{|l|l|l|l|}
\hline & \begin{tabular}{l}
Own a \\
graphing \\
calculator
\end{tabular} & \begin{tabular}{l}
Do not own a \\
graphing \\
calculator
\end{tabular} & Totals \\
\hline Girls & 12 & 6 & 18 \\
\hline Boys & 5 & 7 & 12 \\
\hline Totals & 17 & 13 & 30 \\
\hline
\end{tabular}


Sagot :

To determine the probability that a randomly chosen student will be a girl given that the student does not own a graphing calculator, follow these steps:

1. Identify the subset of students who do not own a graphing calculator.
- According to the table, there are a total of 13 students who do not own a graphing calculator.

2. Count the number of girls who do not own a graphing calculator.
- From the table, we can see that 6 girls do not own a graphing calculator.

3. Use the definition of conditional probability to find the probability that a student is a girl given that they do not own a graphing calculator. The formula for conditional probability is given by:
[tex]\[ P(\text{Girl} | \text{No Calculator}) = \frac{\text{Number of girls who do not own a calculator}}{\text{Total number of students who do not own a calculator}} \][/tex]

4. Substitute the values from the table into the formula:
[tex]\[ P(\text{Girl} | \text{No Calculator}) = \frac{6}{13} \][/tex]

5. Now we'll express this probability as a fraction and also convert it to a decimal form. Since [tex]\(\frac{6}{13}\)[/tex] is already in its simplest form:

- The fractional form is: [tex]\(\frac{6}{13}\)[/tex]

6. For completeness, let's write it as a decimal as well:
[tex]\[ P(\text{Girl} | \text{No Calculator}) \approx 0.46153846153846156 \][/tex]

Thus, the probability that a randomly chosen student will be a girl given that the student does not own a graphing calculator is:
[tex]\[ \boxed{\frac{6}{13}} \approx 0.4615 \][/tex] (rounded to four decimal places).