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
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
A tray of eggs contains 18 large-sized and 12 small-sized eggs. An egg is selected at random. Find the probability of selecting:
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
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
Neither a small-sized nor a large-sized egg.
The eggs are either large or small. It is impossible to select any other size.
