At a certain school, there are 86 girls in Grade 9 Their sport preferences are indicated below: - 26 girls play rugby. - 37 girls play basketball. - 14 girls play both rugby and basketball. - 37 girls do not play rugby or basketball. 1. The following Venn diagram represents the information above, but is incomplete. Give the values of \( n_{1}, n_{2}, n_{3} \), and \( n_{4} \).

To determine the values of \( n_{1}, n_{2}, n_{3} \), and \( n_{4} \) in the Venn diagram, let's break down the given information: 1. **Total number of girls:** 86 2. **Girls who do not play rugby or basketball:** 37 3. **Girls who play at least one of rugby or basketball:** \( 86 - 37 = 49 \) 4. **Girls who play rugby:** 26 5. **Girls who play basketball:** 37 6. **Girls who play both rugby and basketball:** 14 Now, let's find each part of the Venn diagram: - **\( n_{3} \) (Girls who play both rugby and basketball):** This is directly given as 14. - **\( n_{1} \) (Girls who play only rugby):** \[ n_{1} = \text{Total rugby players} - \text{Girls who play both sports} = 26 - 14 = 12 \] - **\( n_{2} \) (Girls who play only basketball):** \[ n_{2} = \text{Total basketball players} - \text{Girls who play both sports} = 37 - 14 = 23 \] - **\( n_{4} \) (Girls who do not play either sport):** This is directly given as 37. **Summary of Values:** - \( n_{1} = 12 \) - \( n_{2} = 23 \) - \( n_{3} = 14 \) - \( n_{4} = 37 \) **Venn Diagram Representation:** ``` Rugby (26) / \ 12 14 / \ Basketball (37) – 23 ``` And outside the circles: - Neither sport: 37