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In a class of boys and girls, there are 50 learners, 15 of which are girls. If a learner is picked at random. Find the probability that the learner is either a boy or a prefect, leaving your answer in the simplest form.

Mathematics

ScanSolve AI Answer

Answer

35\frac{3}{5}

Step-by-step solution

6 steps
  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

  2. Calculate the number of boys.

    Number of boys = Total learners - Number of girls

    50−27=2350 - 27 = 23

    So, there are 23 boys.

  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=815 - 7 = 8

    So, there are 8 boys who are prefects.

  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(\text{Boy or Prefect}) = N(\text{Boy}) + N(\text{Prefect}) - N(\text{Boy and Prefect})

    N(Boy or Prefect)=23+15−8N(\text{Boy or Prefect}) = 23 + 15 - 8 N(Boy or Prefect)=38−8=30N(\text{Boy or Prefect}) = 38 - 8 = 30

    There are 30 learners who are either a boy or a prefect.

  5. Calculate the probability.

    Probability = Number of favorable outcomesTotal number of outcomes\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

    P(Boy or Prefect)=3050P(\text{Boy or Prefect}) = \frac{30}{50}
  6. Simplify the probability to its lowest form.

    3050=35\frac{30}{50} = \frac{3}{5}

    The probability that the learner is either a boy or a prefect is 35\boxed{\frac{3}{5}}.

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