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
Here are the solutions to the questions based on the Venn diagram. The Venn diagram shows the number of guests who drank Mirinda (M) and Coca-Cola (C) soda. • Guests who took Mirinda only: 3m - 6 • Guests who took both Mirinda and Coca-Cola: 6 • Guests who took Coca-Cola only: m + 1 • Guests who took neither: m The condition given is: "If those who took Mirinda but not Coca-Cola are equal to those who did not take Mirinda." Step 1: Translate the given condition into an equation. "Those who took Mirinda but not Coca-Cola" is the number of guests who took Mirinda only, which is 3m - 6. "Those who did not take Mirinda" includes guests who took Coca-Cola only and those who took neither. This is (m + 1) + m. So, the equation is: 3m - 6 = (m + 1) + m Step 2: Solve the equation for m. 3m - 6 = 2m + 1 Subtract 2m from both sides: 3m - 2m - 6 = 1 m - 6 = 1 Add 6 to both sides: m = 1 + 6 m = 7 Step 3: Calculate the number of guests in each region using m=7. • Guests who took Mirinda only: 3(7) - 6 = 21 - 6 = 15 • Guests who took both Mirinda and Coca-Cola: 6 • Guests who took Coca-Cola only: 7 + 1 = 8 • Guests who took neither: 7 Step 4: Answer part a). a) Find the number of guests who took Mirinda only. The number of guests who took Mirinda only is 3m - 6. 3(7) - 6 = 21 - 6 = 15 The number of guests who took Mirinda only is 15. Step 5: Answer part b). b) Find the probability that the next guest to graduate took only one type of soda. First, calculate the total number of guests: Total guests = (Mirinda only) + (Both) + (Coca-Cola only) + (Neither) Total guests = 15 + 6 + 8 + 7 = 36 Next, calculate the number of guests who took only one type of soda: Only one type = (Mirinda only) + (Coca-Cola only) Only one type = 15 + 8 = 23 Finally, calculate the probability: P(Only one type) = Number of guests who took only one typeTotal number of guests P(Only one type) = (23)/(36) The probability that the next guest to graduate took only one type of soda is (23)/(36). Drop the next question.