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Probability

  • If there are n possible outcomes and r required outcomes, the probability, p, of obtaining a required outcome is given as a fraction:
    • Probability, P = Number of required outcomes/Number of possible outcomes = r/n
    • where:
      • P lies between 0 and 1, and
      • P may be expressed as a common fraction, a decimal fraction, or percentage.
  • If an outcome is certain to happen, its probability is 1.
  • If an outcome is not certain to happen, its probability is 0.
  • If the probability of an event happening is p, then the probability of the event not happening is 1 – p.
Examples
  1. It is known that out of every 1000 new cars, 50 develop a mechanical fault in the first three months. What is the probability of buying a car that will develop a mechanical fault within three months?
    • Number of cars developing faults = 50
    • Number of cars altogether = 1000
    • Probability of buying a faulty car = 50/1000
    • ∴ P = 1/20
  2. A tray of eggs contains 18 large-sized and 12 small-sized eggs. An egg is selected at random. Find the probability of selecting:
    1. a small-sized egg.
      • The total number of eggs in the tray = 30
      • Number of small-sized eggs = 12
      • ∴ The probability of selecting a small-sized egg = 12/30
      • ∴ The probability of selecting a small-sized egg = 2/5
    2. either a small-sized or a large-sized egg.
      • It is certain that either a small-sized egg or a large-sized egg will be selected.
      • ∴ P = 30/30 = 1
    3. Neither a small-sized nor a large-sized egg.
      • The eggs are either large or small. It is impossible to select any other size.
      • ∴ P = 0/30 = 0
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