• 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