This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's solve this problem step-by-step. Given: Total students = 200 Students who passed Maths (M) = 160 Students who passed Science (S) = 150 Students who did not pass anything = 10 Step 1: Calculate the number of students who passed at least one subject. Total students = (Students who passed at least one subject) + (Students who passed nothing) 200 = (Students who passed at least one subject) + 10 Students who passed at least one subject = 200 - 10 = 190 Step 2: Calculate the number of students who passed both Maths and Science. We use the formula for the union of two sets: |M U S| = |M| + |S| - |M ∩ S| Where |M U S| is the number of students who passed at least one subject, |M| is the number who passed Maths, |S| is the number who passed Science, and |M ∩ S| is the number who passed both. 190 = 160 + 150 - |M ∩ S| 190 = 310 - |M ∩ S| |M ∩ S| = 310 - 190 |M ∩ S| = 120 Step 3: Calculate the number of students who passed only Maths. Students who passed only Maths = (Students who passed Maths) - (Students who passed both Maths and Science) Only Maths = 160 - 120 Only Maths = 40 Step 4: Calculate the number of students who passed only Science. Students who passed only Science = (Students who passed Science) - (Students who passed both Maths and Science) Only Science = 150 - 120 Only Science = 30 i) Represent the following in a Venn diagram Let M be the set of students who passed Maths and S be the set of students who passed Science. The Venn diagram would show two overlapping circles. • The overlapping region (intersection M ∩ S) contains 120 students (passed both). • The part of circle M that does not overlap with S contains 40 students (passed only Maths). • The part of circle S that does not overlap with M contains 30 students (passed only Science). • Outside both circles, there are 10 students (passed nothing). (Check: 40 + 120 + 30 + 10 = 200 total students) ii) Find the number of students who a) passed both math and science From Step 2: The number of students who passed both Maths and Science is 120. b) passed only maths From Step 3: The number of students who passed only Maths is 40. c) passed only science From Step 4: The number of students who passed only Science is 30. What's next? 📸