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 A be the set of people who liked Ampese, B be the set of people who liked Banku, and F be the set of people who liked Fufu. The total number of people is 20. Given information: N(A) = 8 N(B) = 12 N(F) = 12 N(A F) = 5 N(B F) = 6 N(only A) = 2 N(A B F) = 3 We will fill the Venn diagram regions step-by-step. Step 1: Fill the intersection of all three sets. The number of people who liked all three foods is given: N(A B F) = 3 Step 2: Fill the intersections of two sets only. People who liked Ampese and Fufu only: N(only A F) = N(A F) - N(A B F) = 5 - 3 = 2 People who liked Banku and Fufu only: N(only B F) = N(B F) - N(A B F) = 6 - 3 = 3 To find people who liked Ampese and Banku only, we use N(A): We know N(A) = N(only A) + N(only A B) + N(only A F) + N(A B F). 8 = 2 + N(only A B) + 2 + 3 8 = 7 + N(only A B) N(only A B) = 8 - 7 = 1 Step 3: Fill the regions for only one type of food. People who liked Ampese only is given: N(only A) = 2 People who liked Banku only: We know N(B) = N(only B) + N(only A B) + N(only B F) + N(A B F). 12 = N(only B) + 1 + 3 + 3 12 = N(only B) + 7 N(only B) = 12 - 7 = 5 People who liked Fufu only: We know N(F) = N(only F) + N(only A F) + N(only B F) + N(A B F). 12 = N(only F) + 2 + 3 + 3 12 = N(only F) + 8 N(only F) = 12 - 8 = 4 Step 4: Check the total number of people. Sum of all regions: 2 (only A) + 5 (only B) + 4 (only F) + 1 (only A and B) + 2 (only A and F) + 3 (only B and F) + 3 (A and B and F) = 20. This matches the total number of people in the house, so no one liked none of the foods. a) Illustrate the information on a Venn diagram. A Venn diagram with three overlapping circles (Ampese, Banku, Fufu) would show the following values in each region: Only Ampese: 2 Only Banku: 5 Only Fufu: 4 Only Ampese and Banku: 1 Only Ampese and Fufu: 2 Only Banku and Fufu: 3 Ampese, Banku, and Fufu: 3 b) Find the number of people who liked: i) only fufu The number of people who liked only fufu is N(only F). N(only F) = 4 The number of people who liked only fufu is 4. ii) only one type of food This is the sum of people who liked only Ampese, only Banku, and only Fufu. N(only one type of food) = N(only A) + N(only B) + N(only F) N(only one type of food) = 2 + 5 + 4 = 11 The number of people who liked only one type of food is 11. Send me the next one 📸