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PROBABILITY FOR STATISTICS GCE O LEVELS/IGCSE

INTRODUCTION

The word probability has two basic meanings: (i) a quantitative measure of uncertainty and (ii) a measure of belief in a particular statement or problem. Probability and statistics are fundamentally interrelated

EXPERIMENT

A Process which gives some results.

RANDOM EXPERIMENT

An experiment which produced different results is called random experiment. The result obtained from an experiment or is called an outcome. Drawing of a card from a well shuffled deck of 52 playing cards are example of random experiment. A random experiment has three properties.

1. The experiment can be repeated any number of times.
2. The experiment always has two or more possible outcomes.
3. The out comes of each repetition is unpredictable.

SAMPLE SPACE

The set of all possible outcomes from a random experiment is called sample space.

EVENT

It is an individual outcome or any number of outcomes of a random experiment.

Simple event: An event that contains exactly one sample point is called simple event. Example in tossing coin head is an event and tail is also an event.

MUTUALLY EXCLUSIVE EVENTS

In some situations two events cannot occur at the same time. These events are called mutually exclusive events. In this case:

P(A ∩ B) = 0

P(A or B) = P(A) + P(B)

EXHAUSTIVE EVENT

Events are said to be exhaustive when the union of mutually exclusive events is the entire sample S.

INDEPENDENT EVENTS

When the probabilities of certain events occurring are quite unconnected to one another, these events are said to be independent events.

P(A ∩ B) = P(A) x P(B)

P(A and B) = P(A) x P(B)

Author: Saif Kheraj