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
Welcome back LUCKY — missed you this week. To solve this problem, we first need to determine the number of students in each category using the given information. Let F be Football, N be Netball, and B be Basketball. Given: Total students = 100 |F| = 40 |N| = 45 |B| = 50 |F N| = 24 |F B| = 18 |B N| = 19 Number of students who played none of the games = 18 Step 1: Calculate the number of students who played at least one game. The number of students who played at least one game is the total number of students minus those who played none. |F N B| = Total students - Students playing none |F N B| = 100 - 18 = 82 Step 2: Calculate the number of students who played all three games (|F N B|). We use the Principle of Inclusion-Exclusion: |F N B| = |F| + |N| + |B| - (|F N| + |F B| + |B N|) + |F N B| Substitute the known values: 82 = 40 + 45 + 50 - (24 + 18 + 19) + |F N B| 82 = 135 - 61 + |F N B| 82 = 74 + |F N B| |F N B| = 82 - 74 = 8 So, 8 students played all three games. Step 3: Calculate the number of students who played exactly two games. • Students playing exactly F and N: |F N| - |F N B| = 24 - 8 = 16 • Students playing exactly F and B: |F B| - |F N B| = 18 - 8 = 10 • Students playing exactly B and N: |B N| - |F N B| = 19 - 8 = 11 Total students playing exactly two games = 16 + 10 + 11 = 37. Step 4: Calculate the number of students who played exactly one game. We can find this by subtracting the number of students playing exactly two games and exactly three games from the total number of students playing at least one game. Exactly one game = |F N B| - (Exactly two games) - (Exactly three games) Exactly one game = 82 - 37 - 8 = 37 So, 37 students played exactly one game. a) Basing on the calculation from the information given, advise whether the school should offer sports bursaries. Condition 1: More than 60% play at least one of the games. Number of students playing at least one game = 82. Percentage = (82)/(100) × 100\% = 82\%. Since 82\% > 60\%, this condition is met. Condition 2: More than 40% must know how to play at least two of the three games. Number of students playing at least two games = (Exactly two games) + (Exactly three games) Number of students playing at least two games = 37 + 8 = 45. Percentage = (45)/(100) × 100\% = 45\%. Since 45\% > 40\%, this condition is met. Since both conditions are met, the school should offer sports bursaries. The school should offer sports bursaries. b) Calculate the probability that a student picked at random played only one sport game. The number of students who played only one sport game is 37. The total number of students is 100. P(only one sport game) = Number of students playing only one sport gameTotal number of students P(only one sport game) = (37)/(100) (37)/(100) Send me the next one 📸