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
Step 1: Identify composite numbers among the marks. A composite number is a positive integer that has at least one divisor other than 1 and itself. The marks are 15, 16, 17, 18, 19, 20. • 15 is composite (3 × 5). • 16 is composite (4 × 4). • 17 is prime. • 18 is composite (2 × 9). • 19 is prime. • 20 is composite (4 × 5). The composite marks are 15, 16, 18, and 20. Step 2: Determine the frequencies for the composite marks. From the previous problem, we found x=3. The frequencies are: • Mark 15: Frequency = 6 • Mark 16: Frequency = x^2-1 = (3)^2-1 = 9-1 = 8 • Mark 17: Frequency = 3x = 3(3) = 9 • Mark 18: Frequency = 10 • Mark 19: Frequency = 3x-2 = 3(3)-2 = 9-2 = 7 • Mark 20: Frequency = 5 The frequencies for the composite marks are: • Frequency for mark 15 = 6 • Frequency for mark 16 = 8 • Frequency for mark 18 = 10 • Frequency for mark 20 = 5 Step 3: Calculate the total number of students who scored composite marks. Total number of students with composite marks = 6 + 8 + 10 + 5 = 29. Step 4: Calculate the probability. The total number of students in the class is 45 (from the previous problem). The probability that a randomly selected student scored a composite mark is the ratio of the number of students with composite marks to the total number of students. P(composite mark) = Number of students with composite marksTotal number of students P(composite mark) = (29)/(45) The probability that the mark scored by the student is composite is *(29)/(45). That's 2 down. 3 left today — send the next one.