Answer :
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).
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).
