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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