To determine the probability that a randomly chosen student will be a girl given that the student does not own a graphing calculator, we'll go step-by-step through the information provided in the table.
1. Identify the relevant students:
- We are interested in students who do not own a graphing calculator. From the table, we see that 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:
- According to the table, there are 6 girls who do not own a graphing calculator.
3. Set up the conditional probability formula:
- The probability (P) that a randomly chosen student is a girl (G) given that the student does not own a graphing calculator (C') is calculated using the formula of conditional probability:
[tex]\[ P(G \mid C') = \frac{\text{Number of girls who do not own a graphing calculator}}{\text{Total number of students who do not own a graphing calculator}} \][/tex]
4. Substitute the values:
- Number of girls who do not own a graphing calculator (numerator) = 6
- Total number of students who do not own a graphing calculator (denominator) = 13
5. Calculate the probability:
- [tex]\[ P(G \mid C') = \frac{6}{13} \][/tex]
6. Express the result as a fraction and a decimal:
- The fraction [tex]\(\frac{6}{13}\)[/tex] cannot be reduced further as 6 and 13 have no common factors other than 1.
- The decimal representation of [tex]\(\frac{6}{13}\)[/tex] is approximately 0.4615 (rounded to four decimal places).
Therefore, the probability that a randomly chosen student will be a girl given that the student does not own a graphing calculator is [tex]\(\frac{6}{13}\)[/tex], which is approximately 0.4615.
