#### 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.

- Probability, P =
- 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__

__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.
- ∴ P =
^{0}/_{30}= 0

- a small-sized egg.