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 the given information. Total number of learners = 50 Number of girls = 27 Number of prefects = 15 Number of girls who are prefects = 7 Step 2: Calculate the number of boys. Number of boys = Total learners - Number of girls 50 - 27 = 23 So, there are 23 boys. Step 3: Calculate the number of boys who are prefects. Number of boys who are prefects = Total prefects - Number of girls who are prefects 15 - 7 = 8 So, there are 8 boys who are prefects. Step 4: Determine the number of learners who are either a boy or a prefect. We use the principle of inclusion-exclusion: N(Boy or Prefect) = N(Boy) + N(Prefect) - N(Boy and Prefect) N(Boy or Prefect) = 23 + 15 - 8 N(Boy or Prefect) = 38 - 8 = 30 There are 30 learners who are either a boy or a prefect. Step 5: Calculate the probability. Probability = Number of favorable outcomesTotal number of outcomes P(Boy or Prefect) = (30)/(50) Step 6: Simplify the probability to its lowest form. (30)/(50) = (3)/(5) The probability that the learner is either a boy or a prefect is (3)/(5). 3 done, 2 left today. You're making progress.